What do earworms and the number 1.0594630943592952645618252949463417 have in common?

they’re both long and slimy?

Is it the number of beats per second necessary to make a melody a true earworm?

They both exist in your question?

They are both earrational

Good question. Googling this question, I read about phonological loops, which led me to the term “ostinato.” I have no idea of the correleation, but the scenery’s interesting…

Let’s wait for a few more suggestions, but I promise to give you my solution of this puzzle later. Phonological loops are a good start.

I am in a hurry right now and really shouldn’t be Fluthering, but I can provide a headstart for the future answerers:

Earworm aka last song syndrome “is a term for a portion of a song or other musical material that repeats compulsively within one’s mind, known colloquially as “music being stuck in one’s head” source

Phonological loop (or “articulatory loop”) as a whole deals with sound or phonological information. It consists of two parts: a short-term phonological store with auditory memory traces that are subject to rapid decay and an articulatory rehearsal component that can revive the memory traces. source

The key idea being that it remembers sounds in a certain order and then keeps repeating the order endlessly like a broken tape recorder.

As for 1.059…, uhhh that might be some sort of fluency related variable that is optimum to create Earworms? If so, more $$$ for music artists if they can make use of that. This ridiculously long dissertation by Mizera probably has the answer to this Q in it. But I don’t have the time to read it right now.

Good question!!

@PnL – You’re definitely going in the right direction including the “optimum to create earworms” part, which has a somewhat different meaning, though.

I did a Google search on 1.0595 and found that it is the ratio of frequencies of successive musical notes. Whether this has anything to do with earworms or is just a coincidence I could not say.

The number 1.0595…, as far as I could calculate it, is definitely the 12th root of 2, so it would indeed seem to be related to successive frequencies.

ohhh I thought the question said “EARTHWORMS” haha now I look so silly.

Well, an earworm might actually look like an earthworm, metaphorically speaking of course.

This is an impossible question! Phi on you, @mattbrowne!

The correlation between the two is that they both would make my head hurt!

Yes, Matt. Phi on you! The curse of the golden ratio.

Well, two people saw a connection. One send me a PM to avoid spoilers. Just curious, are those kind of brain teasers part of the set of acceptable Fluther questions? Well, the moderators didn’t intervene, but I’m wondering how Flutherites feel about it.

@mattbrowne Since you asked, I’ll give you a response. Personally, I don’t really enjoy these questions. I prefer questions that someone asked because they’re curious, not questions asked where you know the answer already. But it’s a different spice, maybe I’m just not used to it :)

@dynamicduo – You see, I’m still trying to get a deeper understanding of the Flutherite culture. I’m still fairly new around here. So I’m experimenting. First, I vary the type of question to find out about reactions. Second, I vary the subjects to find out about the interests of people. Who is an expert in what? I add many to “my fluther” to see their questions too. On wis.dm if people didn’t enjoy a certain type of question they simply ignored it and moved on to the next one. Puzzles sometimes triggered highly interesting discussions. And we had lots of fun too.

Of my last 24 questions (see below) I only knew one answer for certain, namely for this one about the earworms. For three others I roughly knew the answer, but am not sure about the details and eager to connect with experts on Fluther (like I did on wis.dm) for example the way the moon slows down the Earth’s rotation increasing the length of each day on Earth. Is the 2 ms per 100 years really a constant? I’m having doubts and couldn’t find anything via Google. If you like you could browse through this list and share with me which questions you think don’t fit into the Fluther culture or would most likely annoy people:

Only a good diagnosis can lead to the right treatment: How many investment bankers engaged in proprietary trading actually suffer from a special form of gambling addiction?

50% of all human beings who are more intelligent than you are female – Why are some men surprised by this observation?

Kartoo and other next-generation search engines with visual interfaces – Why do most people stick with traditional result lists?

Caffeine doesn’t create strong physical addiction, in other words it’s relatively easy to stop taking caffeine. Why do many people compare it to drugs like nicotine or alcohol?

Being alive and dead at the same time – Why are some animal activists outraged by Schroedinger’s cat experiment?

Can you answer the following Fermi question: How many people worldwide are having sex right now this minute?

What do earworms and the number 1.0594630943592952645618252949463417 have in common?

Why do so many people think that natural pharmaceutical ingredients (taken from plants) are safer than artificial pharmaceutical ingredients?

Sometimes the emotional stress resulting from fear of minor dangers is more harmful than the danger itself. Do you agree?

Nothing can touch the freedom of your inner thoughts – Do you really believe that?

Machine translation and a great many funny examples – When can we expect better results for the automatic translation of text from one language (e.g. English) into an other?

Why are most stars in the Milky Way much smaller than our Sun?

How reliable are our alarm clocks – When will the length of a day be 26 hours?

Life is about being yourself – Why do so many people pretend to be someone else?

Using Way-Back-Machines: The Internet Archive is building a digital library of Internet sites and other cultural artifacts in digital form – Will wis.dm and Fluther content be preserved for the next 50 years?

A truck has to make deliveries in 50 cities. Can a clever computer program find the shortest, most economic round-trip route?

Thinking about weird stuff – What is your favorite thought experiment?

Respecting someone’s beliefs does not mean you have to like them – Why are there so many heated debates about different belief systems?

Science fiction will never run out of ideas – the only limiting factor is human imagination. Do you agree?

What if we could slow down the aging process, halt it entirely, or even reverse it – What would this mean for our society?

What is your favorite paradox?

A colorful variety: white dwarfs, yellow dwarfs, orange dwarfs, red dwarfs, brown dwarfs, black dwarfs, red giants, blue supergiants – What is your favorite object in the night sky?

A vision is a dream with a deadline – What is your favorite vision of the future?

Why is the legal minimum drinking age in the United States higher than in Europe?

Connecting with people on the web – Is being on Fluther more time consuming than blogging?

@mattbrowne – I completely understand your actions, and don’t fault you for any of them at all. You’re I think one of the few people actively testing the waters now.

I don’t presume to speak for all of Fluther nor know what the definitive Fluther Culture is (if there is even such a thing). I’ve only been here a few months, after all. But seeing as you seem to take value from my opinion, I’m willing to share it with you as much as you’d like to hear :)

The types of questions best enjoyed here, in my experience, are ones where many people can contribute. Right off the bat, that eliminates a lot of your questions, as many of them rely on advanced or specific knowledge in certain fields (or at least appear to require such). I really don’t think there are a lot of true blooded “experts” who reside here, certainly not more than the number of average Joes.

Another thing that is different with your questions is your format. You tend to follow [Statement] – [Related Question?] followed by details which may or may not be relevant to the question, but which often feel copied and pasted. I can’t help but feel a lack of connection when I open up a question and see a block of text such as in this question. No offense, but I don’t find a wall of text like that to be desirable to read!
Additionally, sometimes your [Statememt] section can be a bit tone setting. I find this extremely off-putting – I prefer to come into a thread without being prejudiced in any way, but such a statement as you included in your caffeine question can’t help but cause just this.

I feel some of your questions may get a better reception if you hold back your opinion and open it up before coming in to the discussion and making a contribution.

Of course, then there’s the issue that many of your questions tend to be theoretical in nature, or having no actual purpose or result. I prefer to answer questions where people actually have a problem or query, and while participating in theoretical discussion is fun sometimes, I don’t get a lot of value from them because not being a subject expert there’s not a whole lot I can contribute, nor do I feel gratified when I make such contributions. This is in comparison to a question where someone is asking how to learn web design for instance, where I can relate my personal experience and true “expertise” and I feel that my answers have value when the question asker and I engage in a dialog. If/when the same user asks a related question, and it shows they are trying their best and making progress in their goals, I feel even more value in contributing to an answer, and it continues.

Looking at one question in specific, the Earth becoming 26 hours per day one. You already had substantially more knowledge than most people coming into it, but you didn’t really share this, although you did make mention of the moon, which confused people who weren’t up to your level of understanding that the moon is a large contributor to the Earth’s rotational speed. I feel your discussion would have been better had you presented your facts at the start, then most of the off topic comments would have been avoided. But your question wasn’t resolved after you had posted your proof, and I think this is simply because no one really knows what will happen, and we don’t have any credentials to make any type of educated guess, so I doubt people saw any value in contributing to that question.

Again, all this is simply my one opinion, and I’d love to keep answering any questions you have.

@mattbrowne , This is a large community with many different types of people. In general, people attracted to a site like this are going to be fairly well educated. There are a fair number of us here who are tech savvy to one degree or another and I see nothing wrong with directing questions to this group. It is also perfectly legitimate to pose a brain teaser type of question. I have done so a few times.

Now when are you going to finally give us the solution to this puzzle?

@mattbrowne, Wait, you came with the wis.dm relocation movement? You mean you haven’t always been a Flutherite? :-)

The solution to the puzzle i.e. answer to the question ‘What do earworms and the number 1.0594630943592952645618252949463417 have in common?’ is

‘well-tempered music’ or ‘well-tempered melodies’.

I’m making the assumptions that earworms, the sort of addictive melodies circling in the human brain’ were played with well-tempered instruments like e-pianos (discounting the capability of violinists to play non-well tempered melodies were the ratio of frequencies of a quint for example can be 3 to 2).

The irrational number is 2^(1/12). Suppose you start at 440 hertz. The frequency of the next note is 440 times 2^(1/12) and so forth till you reach 880.

Does this help?

@AlfredaPrufrock – Yes, I did. I had been a wis.dm-er for more than 18 months before becoming a Flutherite.

@dynamicduo – Thanks for taking the time to share your thoughts. I understand your point of view, but for some of the points you made I have a different opinion. Maybe instead of the word “expert” I should have used “people with advanced knowledge”. Like I did on wis.dm I try to create about one third of my questions in a way that allows everyone to contribute. But that’s it. If the expectation is all of them, then Fluther is probably not the right community for me. On wis.dm we had categories like “culture” and “science and technology” and “environment” (the creators called them scenes). I was most active in “science and technology”.

Because 2/3 of my questions are advanced I often use definitions copied from somewhere on the web (in most cases Wikipedia). On wis.dm there were always 4 entry fields, 3 identical to Fluther and a fourth for the URL of the source. I could just post a Wikipedia link in the details field but it’s my experience that many people don’t like to switch between two browser windows or tabs too often. If this is important to you I can copy both a definition or some other snippet and paste in the link as well.

I like questions like ‘How reliable are our alarm clocks – When will the length of a day be 26 hours?’ and I think it doesn’t really matter how much knowledge I already have. The real question behind this is ‘Why are people surprised that so many things we take for granted do change?’ The whole universe is changing constantly. Even our Sun has ‘bad moods’ and can mess up things here on Earth. There are “weather” forecasts for solar winds which many people are not aware of. I think it’s great when people are willing to open their minds. It’s great when people realize that science can be a lot more fun than rote learning of formulas. Yet for that you need brain teasers. You need to stimulate the reader. And then very often you get highly interesting discussions. And every discussion is different. If given the choice between ‘What is the color of Paris Hilton’s new dress after she got out of rehab?” and “Why should we all be more interested in math?” many will pick the first one.

I’m not saying there’s no value in observing celebrities struggling with drug problems. But hey, there are far more important issues like how can we keep the homes of all people warm, when the barrel of oil costs $250. Therefore I’m using a question format that sometimes includes statements. A question needs to stimulate both the left and the right part of a human brain (the same holds true for convincing other people).

And I’m sometimes copying definitions, because I think it’s a waste of my time to create one using my own words. I use my time to create unique comments like this one.

@mattbrowne I think, in general, this website is best suited for non-advanced knowledge questions. There is no expectation of anything here beyond fitting in with the guidelines, and it is solely up to you to decide what questions you desire to post, however I fear that if you keep asking the same themed questions you ask now, the responses in the threads will not be what you desire.

Some of your questions seem to take the aim of educating other people, or as you say, “You need to stimulate the reader.” That’s not the purpose of this website at all, though, and I can’t help but feel that when you do this you are standing on a soapbox, and I do not find this appealing. It’s like you have a lot of knowledge and wish to directly share it with people. This is what a blog is best suited for, not Fluther. As well, the copying and pasting of definitions rubs me the wrong way with a big hand. There’s no need to copy and paste a definition when you can create a link to it!

With all due respect, I almost guarantee you that most people saw your 26 hour question, realized they did not have the knowledge to answer, and passed it by. The conversation in that thread died a slow and miserable death, I feel.

When you use questions with statements, I feel that you already have a strong opinion on the subject and you inadvertently set the tone of the thread. As I said, this is problematic when the statement you say is provably false, or not even related to the question at hand (the statement portion of the 26 hour question). I feel that you come into your questions with an agenda, and this is markedly different from the majority of questions asked. I say majority and not all, because there are users who ask ambiguous questions, and as long as it fits the guidelines they are generally left.

Your phrase, “A question needs to stimulate both the left and the right part of a human brain” is inconsistent with the general purpose of this website. And who’s to say the value of a Paris Hilton question is lower than one of your scientific ones? It just happens to be that on this site, such generalized and “pointless” questions are the ones that are asked and answered most. I for one do not consider heating other people’s homes to be any of my concern nor care, nor do I see how such a question warrants using leading statements.

@dynamicduo
Maybe. I don’t know your position on this site, if you are a moderator, founder or another user. The intent of this site that you say you have insight in, doesn’t itself set a clear boundary of what is published on it, and initial intent doesn’t mean that intent can’t change. Sure, it is for a moderator to consider, and maybe that’s what you are sharing here.

I agree that the format of his questions are massive sometimes, and could be cut to a smaller ingress with links to add to context.

I see his questions as an opportunity to discuss new and old ideas and it seems that he has a wish for valuable input to contest his views and add to them.

More is not always less. I think that his questions adds to the diversity. And what people don’t interest in, they skip. I think that’s the way it should be. Sure, Paris Hilton yes or no questions are popular. Let someone else write those.

@oratio I have made it clear that I am simply another user of the site. When you visit someone’s profile, you will see a banner indicating if they are a founder or moderator.

@dynamicduo
Cool. Not the point of my comment, but it doesn’t matter. I new here since three days, so I don’t know much about the site at all.

I personally like these types of questions. While not mathematically oriented, I am logic and puzzle oriented.

@dynamicduo:

Reading your last comment makes me feel that I’m also becoming a target like some of my fellow ex-wis.dm-er (the ones who tried to remain polite). I interpret your attitude as a desire aiming at a more homogeneous culture in a sense that diversity and multiculturalism is not what Fluther should be. People who don’t fit, should look elsewhere on the web. I’m just sharing with you how I feel right now, maybe I misunderstood some of your words.

I’m very much aware that my type of questions are not run-of-the-mill Q&A. The same was true on wis.dm, yet the culture there was a bit more tolerant, a bit more forgiving. This also led to a lot of trivia questions. Some people driven by the strange urge to earn points typed in 10 questions in a row like

Do you like cheese type 1?
Do you like cheese type 2?

and so forth. I forgot the actual types, but it was a mixture of American and European regional brands. I thought it was funny and it didn’t bother me for 2 reasons: wis.dm had categories like science & technology and low-response questions trickled down and disappeared quickly.

On the other hand, asking “odd” questions (viewed as odd by some users) wasn’t a problem either, because they didn’t appear in the style or shopping categories. In some categories there was a mix of trivia and advanced questions. The trivia people ignored my questions, which was fine with me. There were still more than a 100 wis.dm users (some immigrated over here as well) who liked my type of questions and the debates they sometimes triggered. They even liked the “education” component in it (“oh, I didn’t know that, thanks for sharing”). Of course one could also become an easy target of trolls and spammers, which is very rare on Fluther and for that I’m very grateful.

If I get the feeling that even over time too many people are bothered by my questions or even accusing me they are not genuine, I would have to accept it and decide whether it makes sense to stay or not. Of course all my questions are genuine. Yes, I love the occasional puzzle or brain teaser for which I already know the answer. If this is totally unwanted here I’d have to give that up.

I’ve already met at least 20 people with intellect and a positive attitude, so I’m quite hopeful once other more critical people get to know me, more online friendships will form. I strongly feel about giving context to challenging questions. Definitions are key. If we are not talking about the same thing, many discussions can become futile. I’m a fan of Wikipedia definitions, because they are the result of a rigorous editorial process. I have no problem to always add the Wikipedia link (or some other link) even though it’s pretty obvious that I was referring to a encyclopedic entry. I’m sorry that I slightly offended or irritated a few people by omitting the explicit link. All my newer questions do have them. On wis.dm it hadn’t been such a big deal and maybe therefore I became a little sloppy about it. I apologize for that. Citing sources is a very good academic practice which I fully support. Fluther aims for high quality and standards and overall that’s a very good thing.

But if Fluther can’t tolerate diversity and peculiarities about individual users, I’m more than eager to leave as soon as possible. So if a lot of people agree with your last post, dynamicduo, I’m out of here.

Fluther has room for all sorts of questions, from the silly to the sublime. Keep right on asking your questions, Matt. Do include a link to your sources, too.

@dynamicduo

I do respect your “seniority” on this site, your lurve and what not, but quite franky, you have just aligned yourself with some of the wis.dm trolls we have recently inherited, if a little more… well versed…

Some people enjoy to ask about cheese brands, some enjoy the fundamental and profound.

I too am a user of this site, and I very much enjoy mattbrownes questions. As a matter of fact, I think he is a great addition of great mind and attitude.

Your response is nothing but abrasive and open hostility disguised as intellectual exchange, MOST CERTAINLY not a reflection of the general sentiment here at this site; and personally, just conjured the image of someone being intimidated by intellect.

I am very much getting the idea that some users that have held a certain “big brain” status are not looking fond at having to share their thrones.

So please, we have now for two weeks accused the majority of wis.dm users of being passively agressive, abrasive, and what not – let’s not fall into the same behavioral pattern.

And on a side note, I remember you either participating or even asking the question if it is okay to post a question if one feels they have the answer already. Your “guideline compliance” there wasn’t nearly as clear cut as you present it here.

Quite frankly, your response was so totally uncalled, I simply lack the capability to remotely understand what was going on in your mind there.

This question , about defining ‘rudeness’ in written word, seems applicable here. We often attach negative intent to the written word that is not necessarily there.

@mattbrowne: I don’t think any one person here is a perfect representative of fluther. We all want different things from the site, and have different preferences about the kinds of questions we like.

I believe there is room for all different kinds of questions. I don’t answer every question (even if it seems like that, lol). I skip the ones that don’t look interesting. I’m sure all of us do that.

If a person is sucked in, and then later decides they don’t like the discussion, they can leave. I’ve done that, too. We don’t have to fight to the death on every disagreement.

FWIW, I think your questions are interesting, when you make it clear what you are asking. You’re new. You’ll learn what questions get a lot of response and which ones get little. Sometimes you may want to ask a question that won’t appeal to many people. That’s fine.

I wonder what you do enjoy about a site like this? Hmmm. I think I’ll ask that.

@daloon – You know what the real reason is: It’s the people I meet. Getting to the bottom of things is important too of course.

And to top it all off, since “guidelines” were mentioned, I think “I’m not answering your question but rather comment on how I feel about such questions” comments certainly have a “special place” there.

@daloon
I enjoy your comments mostly, and you are often very reasonable even when I don’t agree. You seem like a nice person with a good intellect, so I enjoy exchanging comments with you.

But what is in that picture, my brother. It looks like a diseased ass. I keep thinking, “is it his ass?” It looks quite firm, so if so, you have a lovely ass. But what the hell happened to it? First it disturbed me, so I tried to pretend that they were tits. But then I realized something about myself. Diseased tits don’t make me feel good. Not at all! So… Now I don’t now what to do. I think I’ll just pretend that it is a picture of MY ass, and try not to feel creepy about you keeping pictures of me.

@mattbrowne I’m sorry you feel my comment was in any way targeting you or attacking the wis.dm community. That was certainly not my intention. I was expressing the way I felt about this site, as I clearly said in my first comments.

You’re free to do whatever you want with this site. I don’t really care.

Have fun.

@oratio: well, for one thing, it’s not my ass. To me, it looks like a feminine ass. If you want a closer look at it (ok, now I’m cracking up), try this.

Some people say that my ass is tattooed. Personally, I think it’s just a photoshop kind of thing. The ass, by the way, is most probably Russian. I had to search all over the place for it, and in the process I discovered some very interesting Russian websites (not that I kept the URLs), that is, if you happen to be the kind of guy who appreciates the feminine form, preferably unclothed. Arty, yet revealing.

Now, if you really have to think of that ass as your ass and not mine, feel free. We can share an ass. Although the image of one ass with two guys attached to it is pretty amusing. Four legs, four arms, two heads and one ass. Is that a horror story or an alien adventure? And more to the point, is that a title of a book or an album? Or possibly contemporary opera? But I digress.

Anyway, if you really want to pursue this, I would do a google image search on zhopa. Well, I guess I saved you the trouble.

@daloon
Thank you, dear fellow. I will check it out.

I am just glad I don’t live in Mozambique.

@dynamicduo I’ve read your comments here and I am curious: why the whole elaborate explanation? Isn’t there room for Matt-type questions here? Certainly all the people who have commented on his numerous questions would disagree with you!

I personally love them. Most of the time, I don’t understand them, but they challenge me to read on, and usually from the answers and comments, plus a little further reading, I learn about topics I’d never have had the inclination to.

Certainly there is room for Matt’s questions in fluther, and for those who prefer easier or less challenging questions, in any format he so chooses (that pass the moderators) well, the Britney question gallery is over there >>>>>.

@daloon, Lurve for using “ass” and “cracking up” in the same post!

However, I’m crushed to find out that your avatar is not an image of your ass. I had conjured up a tale, that in a rather fanciful fit of darkness, you had the map added to your fanny in order to be able to find your way back home at all times…

Darn. I shall have to transfer my fixations elsewhere…

@AlfredaPrufrock

LOL Alfreda hahaaa

….so Lurve !

This thread appears to have bottomed out.

@daloon Well, I love the ass in your avatar! For some time, I thought you were a lady loon because it looked so scrumptious! :)

I hope that you keep on asking the same types of questions you always have, I may not always understand, but I find them interesting and learn a thing or two along the way. :)

Did we ever learn an answer to the question?

I liked the question. What I found a bit odd was the idea of the questioner knowing the answer and then not telling us; instead we just got clues. This was sort of new for fluther and I think some members, myself included (a bit), found it too mentally challenging. I have zero background in in mathmatics, so things like “12th root of 2” mean nothing to me.
I do, however read all the math related questions here and have always enjoyed them because they have been about someone’s need for assistance with a querry (This one from finkelitis comes to mind) and not a “hey I know this cool fact and I’m not going to tell you” kinda thing. You’ve got to remember that many of us use fluther as a tool, for help in our lives..
Another thing that strikes me as odd is your seemingly scientific approach to the kinds of questions you ask. I’m guessing you have charts somewhere :) It’s fluther. Don’t take it so seriously.
Lastly, I found the Paris Hilton comment a tad degrading. It was almost as if you were suggesting that we here at fluther were more concerned with gossip and trash than with high-minded concepts. I’m sure you might not have meant it to read that way, but it did. I think you might have us painted wrong
Once again, I liked your question. Keep them coming…

@AlfredaPrufrock: Well, you never know with me. My grasp of reality is such that I could easily be mistaken. Perhaps you shouldn’t give up your fantasy so quickly!

@Kelly27 – I will. I’m not upset anymore (see my more recent “Do Flutherites give strong support to new users if they need it?” question).

In time I will have a private talk with dynamicduo to resolve the issue. I won’t tolerate a choice of words that really hurt my feelings and which I see as an attack on my type of mindset and character and my individual peculiarities. I will stick to all Fluther guidelines. I will always remain respectful and polite. I will try to have a balanced view on things. I’m willing to accept feedback. I do take issue when someone crosses the line. Yet I’m also a very forgiving person. It’s an important part of my personal value system.

@breedmitch – Yes, I’m aware that many use fluther as a tool, for help in our lives and I think it’s a good approach (if you have a few close people in real life as well – the virtual world can support but not replace contacts in real life in my opinion). I’d like to point out that some of my questions do have a direct relationship with current real life challenges. Here are three examples: “Sometimes the emotional stress resulting from fear of minor dangers is more harmful than the danger itself. Do you agree?” and “Life is about being yourself – Why do so many people pretend to be someone else?” and “A vision is a dream with a deadline – What is your favorite vision of the future?”

I’m not sure what you mean with seemingly scientific approach.

I take back my Paris Hilton comment. Maybe there was an impulse inside me related to the developing anger that made me write that. I apologize. Everything around us in our lives can be important. It was just this expectation to limit myself to questions that everyone can contribute to. I won’t promise that. I’ll try to keep a good balance. Thanks for your open feedback!

Yes, you did learn an answer to the question. Here’s my solution again (there are indeed others):

The solution to the puzzle i.e. answer to the question ‘What do earworms and the number 1.0594630943592952645618252949463417 have in common?’ is

‘well-tempered music’ or ‘well-tempered melodies’.

I’m making the assumptions that earworms, the sort of addictive melodies circling in the human brain’ were played with well-tempered instruments like e-pianos (discounting the capability of violinists to play non-well tempered melodies were the ratio of frequencies of a quint for example can be 3 to 2).

The irrational number is 2^(1/12). Suppose you start at 440 hertz. The frequency of the next note is 440 times 2^(1/12) and so forth till you reach 880.

Does this help?

@mattbrowne: um, this is a case where a little learning is a dangerous thing.

What you’re talking about is not well temperament but equal temperament. It’s a compromise that means that music sounds identically bad in all keys.

In just tuning, the important notes in the scale have small integer ratios with each other, and if the music is being performed by singers, the pitch level is often constantly being renegotiated. If it’s being performed by fixed-pitch instruments, they’re often keyed instruments – trumpets in B-flat or A, for instance. But this means that one key will sound beautiful and rich, and other keys will sound rather ugly. In particular, the fifth from scale degree 2 to scale degree 6 is considerably smaller than it should be, which makes secondary dominants hideous chords—and even as late as the 1870s, when Bruckner was teaching at the Vienna Conservatory, students were advised to treat the supertonic chord in major as a diminished chord.

But when keyboard instruments started to be more popular, they needed to be able to play in more keys; and when they started being used with choirs, they needed to be able to play at higher and lower pitch levels to match the choirs. So they couldn’t decide, for instance, that this organ would be tuned in C and damn the other keys; they had to work out a tuning system that sacrificed the purity of one key in exchange for acceptable sounds in other keys.

This is where well temperaments come in. There are dozens of these, all experiments. The logical conclusion is dividing everything equally, and that’s where equal temperament comes from—but equal temperament is ugly, and the major third is especially large and ugly in it.

Now, your assumption, I’m afraid, is wrong. People recognize tunes no matter what tuning or temperament they’re played in, and a tune can be catchy even when it’s sung out of tune. It’s not the tuning system that determines the mental stickiness of a jingle, or else every advertiser would be writing ad jingles in just tuning rather than equal temperament.

@cwilbur – Your answer is a wonderfully precise description of the topic. When looking at definitions it’s my understanding that equal temperament is an example of well temperament and I was using the somewhat broader (and maybe a bit more familiar) term when giving my solution of the puzzle about the earworm. There are other forms of well temperament.

From Wikipedia: Well temperament (also circular or circulating temperament) is a type of tempered tuning described in twentieth-century music theory. The term is modeled on the German word wohltemperiert which appears in the title of J.S. Bach’s famous composition, Well-Tempered Clavier. In most tuning systems used before 1700, one or more intervals on the twelve-note keyboard were so far from any pure interval that they were unusable in harmony and were called a “wolf”. Another example of this is equal temperament which is a musical temperament, or a system of tuning in which every pair of adjacent notes has an identical frequency ratio.

There are by the way many other correct answer to my question like: they both use more than 7 alphanumeric characters and so forth. I loved the suggestion “both are long and slimy”.

I’m a computer scientist by profession and music is one of my favorite hobbies. I also like fun questions and I like to meet fun people online. So when I created my question and gave (in your view) a somewhat simplistic solution I have to admit it might not withstand the scrutiny of scientific method. You seem to know far more about music theory than I do and were able to use all terms with greater precision. Yet I know a little bit about first order logic and mathematical set theory. If equal temperament is an example of well temperament it can be seen as a subset. Maybe you can prove me wrong and I guess some veteran Flutherites will applaud you because they are still looking for things we ex-wis.dm-ers are “doing wrong”. Guilty as charged.

This is the historical context. Bach wrote The Well-tempered Clavier, and it’s fairly well understood among musicologists that he meant some sort of meantone tuning. There is a small but strident group of amateur musicologists who play with tuning and edit Wikipedia; though they may include equal temperament among their concept of “well temperament,” I would be amazed if you would find that in any peer-reviewed journal.

So, in essence, your logic in calling equal temperament a well temperament based on that definition is correct, but the premises are flawed, if you intend to connect equal temperament to Bach.

And I see your citation of Wikipedia and cite an expert of my own, Carl Dahlhaus.

He’s discussing the connection between theoretical constructs and audible phenomena in music—and the connection, or lack thereof, between what we understand and what we hear. He gives the example of the 9:8 and 10:9 whole tones (C-D and D-E in just tuning in the key of C) and then goes on to say:

“If the dissociation of the major and minor whole tones is an acoustical difference without a musical correlate, then conversely, in the tonal system of tonal harmony there are musical differences whose acoustical correlate is uncertain or even unimportant. The contrast between diatonic and chromatic semitones [the difference between C-sharp and D-natural, as a diatonic semitone, and D-flat and D, as a chromatic semitone] is musically real without there necessarily being an acoustical presentation of it. The contrast is unmistakable even when an acoustical differentiation is either lacking or opposite to what it should be. Nowhere does the fact that the tuning is irrelevant show itself more clearly than in the habit of emphasizing leading tones, thus in the phrase c’-g#-a raising the g# as though it were a-flat, and in the phrase c’-a-flat-g lowering the a-flat as though it were g#. Notwithstanding the fact that the intonation interchanges g# and a-flat, the musical meaning, the conception of g# as the third above e and of a-flat as the third below c’, is never at risk. [...]

“The indifference of listeners to the acoustical differentiations between major and minor semitones is the basis for justifying 12-tone equal temperament, while the musical irrelevance of the distinction between major and minor whole tones is the basis for justifying methods of mean-tone tuning. On the other hand, the proportion of the perfect [/] fifth is distorted by both mean-tone tuning and equal temperament. Yet however insignificant the deviation may be, it is nonetheless unavoidable. And the fact that when the defect clinging to the acoustical representation of the harmonic tonal system is smoothed over in one place it will always spring up in another is proof of an irreconcilable divergence between tonal system and tuning. There is no “just” intonation—the tuning known by that name suffers from having an acoustical difference between two sizes of whole tones, a difference to which nothing corresponds musically.”

(Carl Dahlhaus, Studies in the Origin of Harmonic Tonality, trans. Robert O. Gjerdingen (Princeton, NJ: Princeton University Press, 1990), 189–90.

He goes on to discuss the same issue in the context of Pythagorean tuning and the debates over tuning, temperament, and intonation in the early Renaissance.

Finally, I don’t think you’re wicked or evil; I think you have a superficial understanding of music theory and a bit too much reliance on Wikipedia, and it’s led you down the wrong path. You can argue logic and get defensive, or you can learn from my response and deepen your understanding of music theory. Which path you choose is entirely up to you.

@cwilbur – Thanks for helping me deepen my understanding of music theory.

Me. too. painful. brain. hurt. but hurt so good.

@Zen – Had a drink, last night?

A few, it’s Passover. Mitzvah. :-)

Mitzvah, my dear friend! For us it’s Good Friday today and we’ll have fish for lunch. It will become unseasonably warm in Germany over Easter. Weather forecast said up to 25 C / 77 F. Finally! It has been a very long and cold winter. Talk about global warming ;-)

For some reason this question popped up in a side bar on June 14 th and I happened to check it out again. I was one of the 2 people who answered it in a PM to not spoil the quest for anyone. I got it by the way. ;-)
I had no idea there was so much controversy. I happen to like the technical questions and through them I’ve met about 1/2 dozen people I’d sure enjoy meeting.
Fermi questions made me think and help me look at the world in a slightly different way.
One of the nice aspects of Fluther is the ability to skip a question if you don’t like it.

@Lupin – Well, some people don’t skip when they don’t like a question. I guess we have to live with it.