Theory Of Harmony: Pi

Bartok and other composers worked with the Fibonacci sequence and the Golden Ratio in their pieces, and inspired by Hans' isochords, I thought I'd create my own harmonic theory!

3.1415926535 8979323846 2643383279 5028841971 6939937510

5820974944 5923078164 0628620899 8628034825 3421170679

8214808651 3282306647 0938446095 5058223172 5359408128

4811174502 8410270193 8521105559 6446229489 5493038196

4428810975 6659334461 2847564823 3786783165 2712019091

4564856692 3460348610 4543266482 1339360726 0249141273

7245870066 0631558817 4881520920 9628292540 9171536436

7892590360 0113305305 4882046652 1384146951 9415116094

3305727036 5759591953 0921861173 8193261179 3105118548

0744623799 6274956735 1885752724 8912279381 8301194912

9833673362 4406566430 8602139494 6395224737 1907021798

6094370277 0539217176 2931767523 8467481846 7669405132

0005681271 4526356082 7785771342 7577896091 7363717872

1468440901 2249534301 4654958537 1050792279 6892589235

4201995611 2129021960 8640344181 5981362977 4771309960

5187072113 4999999837 2978049951 0597317328 1609631859

5024459455 3469083026 4252230825 3344685035 2619311881

7101000313 7838752886 5875332083 8142061717 7669147303

5982534904 2875546873 1159562863 8823537875 9375195778

1857780532 1712268066 1300192787 6611195909 2164201989

These are the first several thousand digits of Pi. Here is basically how it works, using a fixed integer notational system (0 = C), you use the decimals of Pi as an ever changing tone row while using the overtone series of 3 (e-flat) as a drone. E-flat will be constant and can never be changed, but the decimals always change. This way we can have the HEROIC sound of the E-flat and harken back to the days of yore, while at the same time using a RANDOM atonal system not that dissimilar to Arnold Schonberg's developing variation (or Brahms', whoever you want to credit it to).

This is my way of mixing the OLD (heroic E-flat overtone series!) with the NEW (infinite tone row based on the decimals of Pi).

Interesting... But then you're limiting the pitches to C-A, no B or Bb...

I see what you did ther.

Interesting... But then you're limiting the pitches to C-A, no B or Bb...

Every tenth decimal you will add that and the subsequent number, then mod12. For instance...

3.1415926535 8979323846 2643383279

5 is the tenth, and 8 is the eleventh..

8 + 5 = 13

13 mod12 = 1

In this theory....

odd # = B-flat

even # = B-natural

So for this, these two numbers would combine to create B-flat!

My god... you should tell that to Babbitt... No it doesn't.

It is apparent that there are more artistic music composers, and more scientific composers. Perhaps they shouldn't be arguing with each other - it's like trying to mix oil and water. :musicwhistle:

On a side note - I agree with Nico, this kind of defeats the purpose of music as art, in my opinion. But on the other hand, I find more scientifical (yes, I just said that) musical theories rather fascinating and altogether a separate practice, even if I'm not too fond of the results (Babbitt, Schoenberg, and on)

ANY composer is artistic. You shouldn't categorize things like that.

Music based off of numbers/math completely defeats the purpose of art. Stop it.

Can you be more specific, anything can be boiled down to numbers really (binary code, narf, learn history). I think it's dangerous to make the concept of art so ***exclusive***

Point is, there's no point in repeating this argument yet again. Nobody will ever admit defeat to the other.

On a side note - I agree with Nico, this kind of defeats the purpose of music as art, in my opinion. But on the other hand, I find more scientifical (yes, I just said that) musical theories rather fascinating and altogether a separate practice, even if I'm not too fond of the results (Babbitt, Schoenberg, and on)

I don't understand this.... notion... I guess if that is what you could call it... of something being more scientific than something else?? I don't get it. Serialism isn't more.. uh... "scientifical," than geeze... this is just ridiculous. Why am I expecting to have a serious discussion of art with anyone on here who has to have an opinion on everything. Just shuuut it and listen and stop calling everything this or that.

Music based off of numbers/math completely defeats the purpose of art. Stop it.

It is apparent that there are more artistic music composers, and more scientific composers. Perhaps they shouldn't be arguing with each other - it's like trying to mix oil and water. :musicwhistle:

On a side note - I agree with Nico, this kind of defeats the purpose of music as art, in my opinion. But on the other hand, I find more scientifical (yes, I just said that) musical theories rather fascinating and altogether a separate practice, even if I'm not too fond of the results (Babbitt, Schoenberg, and on)

Yup, pitch content is the only artistic part of music.

And serialization doesn't have direct parallels in any number of prior forms.

I'd be interested to see what would come of this -- I'm sure there are some interesting melodies in there...

Okay first let's actually start with some definitions of art...

art1  [ahrt] Show IPA

I apologise - you mistook my more personal feelings for factual arguments. I did not explicitly distinguish. Factually, in the world you can call what ever you want art, I know this. It has been done. Personally, my idea of art music (classical music) is not based on numbers and mathematics. The word "art" to me evokes a very personal affinity for a general assortment of music that speaks to me. It is in my mind that a composer that bases his music on numbers and mathematics is not creating art in the sense that it is an intimate expression of his pure self (or soul, if you will). He is crafting more or less from more scientific algorithms that are preset and that he cannot alter. If you make music from 3.14159... you can not change Pi. You can change a melody, but not a series of numbers without defeating the purpose of using them in the first place. You CHOOSE to use Pi, however, which is as novel an artistic concept as a Brahms symphony, but the music that results in my opinion is less art than an experimental marriage between music and mathematics. These are my feelings - I'm sorry it is such a sin to express personal opinions (no matter how informed) on this site, but I'm not prepared to argue factually and with definitions and nor do I intend to because I feel music is what you yourself as an individual makes it to be, not a definable phenomenon.

It is in my mind that a composer that bases his music on numbers and mathematics is not creating art in the sense that it is an intimate expression of his pure self (or soul, if you will). He is crafting more or less from more scientific algorithms that are preset and that he cannot alter. If you make music from 3.14159... you can not change Pi. You can change a melody, but not a series of numbers without defeating the purpose of using them in the first place.

So the key difference, if I understand you correctly, is the use of preexisting and unalterable source material, and thus basing pitch content on pi is less artistic than basing pitch content on divine inspiration? Just to make sure you're considering all the implications of your philosophical conjecture here, how about other extramusical or extrapersonal sources of inspiration?

When Shostakovich uses the DSCH motif, or Bach the BACH motif (as he himself did consciously at least once, and numerous others have since), is the music suddenly, automatically, moved a few steps down on the spiritual ladder and turned into something less artistic? These motifs in themselves are certainly not an intimate expression of anybody's inner self, they could not have been altered without defeating their purpose, and they're based on something nearly as stereotypically dry, intellectual and boring as numbers: letters.

How about when Messiaen uses birdsong? Birds are cool and look good and live outdoors (oh, and they can fly), so they're not nearly as dull and dead as numbers, which are used by such soulless people as mathematicians and scientists, but the fact remains that Messiaen didn't dig deep into his own soul to make up their songs—the birds did.

The key component in the craft of musical composition, and what makes a master a master, is not where the musical material is found—it is how it's used. I'm sure we can all agree on this. How a few rudimentary ideas are built into a symphony; how the material develops and interacts over time; how eventually the listener is left with the memory of an experience far more profound and meaningful than the individual building blocks themselves. In a narrative such as a novel or play—an art form similar to music in that both are occupied with events occurring over time—the meaning and emotional impact comes not from the characters themselves, but from how they interact, develop and influence each other during the course of the narrative.

With these things in mind, how much does it really matter where the basic building blocks came from?

*sigh*

I believe anything can work as long as you do it right. Arnold Schoenberg wrote some near stuff that I enjoyed: Survivor from Warsaw, for example. Berg wrote a fantastic Violin Concerto. Not to mention Walter Piston and his Flute Sonata and other serial works.

What I'm getting at is, personally I feel 12-tone technique and your pi method are just devices, which, I suppose, if you can make something beautiful and aesthetically pleasing (or at least, emotionally meaningful) then that's fine. To write a piece off numbers for the sake of it being off numbers is not really...well, that's more academic. I propose it will sound just like 12-tone music. Unless you tell them, your audience may not hear a difference.

Wow, it's so easy to forget that a lot of music/art/stuff in the middle ages was ENTIRELY based on numbers and math (Isorhythmic motets, etc etc.)

Indeed,

With these things in mind, how much does it really matter where the basic building blocks came from?

No, it doesn't matter at all. I can get all my music material from observing a frying egg or by analyzing isotope decay rates. In the end it goes into music and without the composer to tell you where it came from it is completely detached from the experience.

The result is what matters, not the method. Often I've seen kids say "number r bad musix" and then they go on to say Bach or other such composers are nice or whatever, yet hello thar full of numbers everywhere. It's, as usual, an ignorant bias that would go away if they actually worked with more different methods of composition.

In fact, you can make a piece of music entirely based on weather patterns of any given day, or Doppler radar images, or tracking the motion of planets, stars, etc. The sources you can use to give you material are practically infinite, nevermind the combination of them. However, sure, it all comes down to subjective interpretation of those things and how it applies to the actual music...but that's the interesting part, as it speaks for the actual music product.

HOWEVER!

Pi theory is the best theory ever both in the results AND in method! Even better than Fnarf, dare I say. In fact I'm writing an opera using it right now (it'll use cow samples and guitar feedback noises!)

lol

When Shostakovich uses the DSCH motif, or Bach the BACH motif (as he himself did consciously at least once, and numerous others have since), is the music suddenly, automatically, moved a few steps down on the spiritual ladder and turned into something less artistic? These motifs in themselves are certainly not an intimate expression of anybody's inner self, they could not have been altered without defeating their purpose, and they're based on something nearly as stereotypically dry, intellectual and boring as numbers: letters.

How about when Messiaen uses birdsong? Birds are cool and look good and live outdoors (oh, and they can fly), so they're not nearly as dull and dead as numbers, which are used by such soulless people as mathematicians and scientists, but the fact remains that Messiaen didn't dig deep into his own soul to make up their songs—the birds did.

With these things in mind, how much does it really matter where the basic building blocks came from?

It is not the basic building blocks with which I am concerned. I find it fine to base an entire piece off a short motive that could have been birdsong, initials, or the consequent honking of several automobile horns in a short period of time. It is when the music is composed entirely mathematically or the composer has to work his way around a constant (such as the notes given by this pi sequence) that it loses my interest as an art. I believe this is a technique called ''through composed'', no? I may be wrong.

It is not the basic building blocks with which I am concerned. I find it fine to base an entire piece off a short motive that could have been birdsong, initials, or the consequent honking of several automobile horns in a short period of time. It is when the music is composed entirely mathematically or the composer has to work his way around a constant (such as the notes given by this pi sequence) that it loses my interest as an art. I believe this is a technique called ''through composed'', no? I may be wrong.

You wouldn't be able to tell the difference unless you were explicitly told how the piece was composed. That's how detached method is from musical product. Likewise, what's the bias against math anyway? I find the old traditional forms (sonatas, etc) FAR more strict in numeric nonsense (repetitions, measure proportions, bla bla bla) than a lot of modern pieces even if they were written using math as inspiration/method.

Oh but then it's ok? If you reduce a lot of traditional music to math formulas (which you surely can,) do they suddenly stop interesting you as "art?"

If you want to include this in a piece of music that still says something and communicates a message or feeling, then more power to you. But the most special music will always be the music that is, in fact, music.

Hear, hear.

The more feeling you put in, the better chance you'll have of getting it out, instead of just writing some patterns and hoping people will see it as something else. That's not how it works.

Hilariously, even if you put over 9000 units of feeling into a piece, people may end up thinking nothing of it. Instead, it can as well be the case that someone who wrote something just by looking at patterns and felt literally nothing, gets a very emotional reaction out of people. In fact music randomly generated by algorithms can pass off as human-composed music just fine, people can't tell the difference.

The audience/people can make whatever they want out of anything, no matter what you do or don't do as a composer, the end result is detached from whatever you thought/did/wanted to do unless you then reattach it later by telling people. Though honestly, people can feel rather passionate about numbers, equations and so on too, so stop trying to perpetuate a stereotype.

Take for instance e=mc^2, it's math right?

Is it only just math?

For the record: I don't advocate using the Pi harmony theory thing, in fact I think it's far too impractical, I just wanted to spark **discussion**, and spark it I did...

Anyway, I have to ask Nico and Enigmus (or whoever else) something; do you subscribe to any line of thinking that isn't spit out by German Romanticists? I'm just curious. The way you seem to think about music, especially Enigmus, smacks of naivete. I mean, your basic argument is "When a composer uses a system based on numbers and not feelings to create music, he is therefore removing the human aspect and element of control from said music." This has a few fundamental flaws...

Forget about the Pi theory for now. When we're talking about 12-tone theory, the composer decides the musical materials right from the beginning, this isn't any different from choosing a key and motives. All musical material is generally derived from said row, so one would say that the composer has a high level of *control* of their music, correct? I kind of tire of this argument so I won't continue much further. Long story short, just because something doesn't sound like your definition of "pretty" or "passionate" doesn't mean that it isn't.

Besides, going back to the Pi thing, has it not occurred to you that maybe you're the ones being a bit pedantic here. Music is more than pitch material, music is more than "a pretty melody I can whistle, jee golly!!" because there's still gesture and movement. I could have the most systematic and robotic pitch system in the world, or have a pre-determined set of numbers, and still make it sound like Mahler, your emo german romantic posterboy for crying about the turnips in his garden dying, because there's just more to music than the pitches. Get over Mahler plz, he's dead.

The thing might be that different things have different values. If you would like to feel overwhelmed by passion, you'd better listen to something Mahler wrote. If you'd want to know how something consieved out of PI sounds, Mahler won't do the trick for you. But maybe you may get overwhelmed by passion in th progress. Everything has it's value, it's up to us to see it in it. So, if you don't see it, it doesn't mean it isn't there. It just means you can't see it (yet).

If you would like to feel overwhelmed by passion, you'd better listen to something Stockhausen wrote.

Fix'd for truth.

Yes? They are? That would be why they included their own name into it. Listen to the 8th quartet by shostakovich? He was planning on killing himself before he wrote that. It's entirely about him and his ridiculous pain...notice the use of the DSCH motif, in fact, the DSCH theme...it's the basis of the entire work. And it's a highly personal emotional thing for him.

Sure it is. But the theme itself is only more significant than any other sequence of four notes because the note names (a very abstract and inaudible thing) coincide with the composer's name (which is also very abstract, and, if you think about it, impersonal; it could have been anything else). I think this is as detached and unmusical as using pi. The meaning and emotion do not come from the letters or the name.

2. Messiaen used birdsong because it must have touched him in some way. Not just because he wanted to turn something into music.

You're probably right. What if he were touched by the beauty of a tone row derived from pi?

3. It's not how a musical idea is developed, it's how an idea is developed. This is an abstract concept, whereas actual thematic material is a fairly left-brained concept. Like I said before, what makes music music is music, not technical development or numbers or anything like that. To quote Mahler: "If I could say something in words, why would I bother trying to say it in music?".

I don't see how we're in disagreement here...

To be perfectly honest, I think you're just disagreeing for the sake of disagreeing, because my post clearly positioned me on the side opposite yours in this discussion. Why is it that internet debates always turn into a two-team effort?

Arguing about what constitutes art is probably the most boring thing in the world.