btw being a physicist, I thought I might add a bit of math info regarding the number of possible melodies, which some here might already know about.

Even if we take a diatonic scale with an 8-note melody or theme, choosen out of 12 chromatic notes with no repetitions, the number of possible combinations are 12!/(12-8)! = 19 million. (the ! refers to the factorial function)

That means even without note repetitions there are 19 million possible diatonic melodies. But of course most of these will not sound pleasant. But even if 1/100th of these are good, we have 200,000 melodies. Now imagine if we add 7 note or 6 note or 5 note melodies, allso variations in rhythm.

There is much room for new music!

Anand

Hi Paul,

This is a fantastic melodic theme (Princess Anna). I love the way you changed the intimate mood suddenly (at 1:23).

Great music and fine orchestration!

Jos

Great variations, excellent playing!

Jos

A wonderful job, Dave, for a most special occasion. Did you (both) perform the music live at the marriage ceremony?

As an accordionist, I like the sound of the instrument and the detailed playing techniques. Very melancholic melody though for a marriage. 😉

Jos

Hi William,

All your melodies presented here are fantastic, as well as the orchestrations. The song is my favourite one.

Jos

@William said:

Here is a another melody -

"There is Dew" by Thomas Hood

A well crafted melody. The entire work is brilliant. The art of crafting melody is a balancing act between repeition and change, familiar structured phrase and surprise, and between dissonance and consonance. Great melodies have a nearly perfect (nothing I suppose is totally perfect) balance of these elements. 

@agitato said:

btw being a physicist, I thought I might add a bit of math info regarding the number of possible melodies, which some here might already know about.

Even if we take a diatonic scale with an 8-note melody or theme, choosen out of 12 chromatic notes with no repetitions, the number of possible combinations are 12!/(12-8)! = 19 million. (the ! refers to the factorial function)

That means even without note repetitions there are 19 million possible diatonic melodies. But of course most of these will not sound pleasant. But even if 1/100th of these are good, we have 200,000 melodies. Now imagine if we add 7 note or 6 note or 5 note melodies, allso variations in rhythm.

There is much room for new music!

Anand

Thank you for sharing this. I was not aware of these numbers. And they do not seem to include a calculation for note durantion (rhythm). I am no mathematician or physicist, so I have no idea how to include duration. Perhaps you could help us. If we also say every one of the 8 notes of the diatonic scale can have a rythmic value of whole note, half note, quarter note, eigth note or sixteenth note, or any of those values as a triplet, how would that alter the calculation?

@Jos Wylin said:

Hi Paul,

This is a fantastic melodic theme (Princess Anna). I love the way you changed the intimate mood suddenly (at 1:23).

Great music and fine orchestration!

Jos

Thank you so much. I get very little feedback (positive or negative) about my music so your comment is much appreciated. The Pricess Anna theme is part of a larger composition, which is finished, but I just cannot get comfortable with the mix. I keep changing it. Thanks Jos.

@William said:

Here is a another melody -

"There is Dew" by Thomas Hood

 

I probably listened to this piece a long time ago, but forgot how beautiful it is, it is truly beautiful William. I love how the orchestration isn't overdone, something there reminds me of Puccini, which I'm a huge fan of. One of the nicest piece I've heard here. 

@agitato said:

btw being a physicist, I thought I might add a bit of math info regarding the number of possible melodies, which some here might already know about.

Even if we take a diatonic scale with an 8-note melody or theme, choosen out of 12 chromatic notes with no repetitions, the number of possible combinations are 12!/(12-8)! = 19 million. (the ! refers to the factorial function)

That means even without note repetitions there are 19 million possible diatonic melodies. But of course most of these will not sound pleasant. But even if 1/100th of these are good, we have 200,000 melodies. Now imagine if we add 7 note or 6 note or 5 note melodies, allso variations in rhythm.

There is much room for new music!

Anand

Thank you for sharing this. I was not aware of these numbers. And they do not seem to include a calculation for note durantion (rhythm). I am no mathematician or physicist, so I have no idea how to include duration. Perhaps you could help us. If we also say every one of the 8 notes of the diatonic scale can have a rythmic value of whole note, half note, quarter note, eigth note or sixteenth note, or any of those values as a triplet, how would that alter the calculation?

Yes I assumed all notes are the same length.

If we want to include whole, 1/4, 1/8, and 1/16th notes,  keeping it still an 8 note melody, we now have 12 x 4 = 48 notes to pick from. So now the calculation is 48!/(48-8)! = 15 trillion. (there is a simpler way to look at this. There are empty 8 slots, and we have 48 apples. The first slot can be filled with any of the 48 apples, second with any of the remaining 47, third with 46, and so on. So we have 48*47*46*45*44*43*42*41 ways of filling the 8 slots, which comes to 15 trillion)

So you can make 15 trillion 8-note melodies with chromatic notes and note lenghts from whole to 16th. Of course many of these will be redundant. For example, if all 8 notes are the same duration, changing from quarter to whole is simply like playing the same melody faster! But if I am not wrong that is only the case for 12 x 4 = 48 melodies.

So that still leaves us with 15 trillion - 48 melodies, which makes the same difference as a turtle peeing in the atlantic ocean. Note that I have left out rests. (John cage will pick all 8 as rest notes. so he wont care about this discussion. LOL)

I still believe there will be many redundancies, but if we can use even 1 millionth of these, it leaves us with a biliion combinations. 

Not bad to be a composer!

Anand

Hi Anand,

Thank you! That answer first made me laugh, then I sort of went into a daze thinking about it. 15 trillion. Wow. Thanks for the help.

Paul

@agitato said:

btw being a physicist, I thought I might add a bit of math info regarding the number of possible melodies, which some here might already know about.

Even if we take a diatonic scale with an 8-note melody or theme, choosen out of 12 chromatic notes with no repetitions, the number of possible combinations are 12!/(12-8)! = 19 million. (the ! refers to the factorial function)

That means even without note repetitions there are 19 million possible diatonic melodies. But of course most of these will not sound pleasant. But even if 1/100th of these are good, we have 200,000 melodies. Now imagine if we add 7 note or 6 note or 5 note melodies, allso variations in rhythm.

There is much room for new music!

Anand

anand, being a physicist myself I have to correct you there 😉: the minimal number of 8-note melodies is 12^8 (taking a melody as an ordered set with repetitions - see guy’s first masterpiece 😃), which is already nearly half a billion. as you point out this does not take into account that notes can have different lengths … as well as different velocities, being played with different articulations, dynamics, vibrato—and changing some of these additional properties you can easily mess up any good melody.

so the odds to find a good melody by chance should be far less than hitting the jackpot. but the amazing examples in this thread (which I enjoyed very much!) show that music is not math and that all these extremely talented people here definitively know what they are doing 😊.

@agitato said:

btw being a physicist, I thought I might add a bit of math info regarding the number of possible melodies, which some here might already know about.

Even if we take a diatonic scale with an 8-note melody or theme, choosen out of 12 chromatic notes with no repetitions, the number of possible combinations are 12!/(12-8)! = 19 million. (the ! refers to the factorial function)

That means even without note repetitions there are 19 million possible diatonic melodies. But of course most of these will not sound pleasant. But even if 1/100th of these are good, we have 200,000 melodies. Now imagine if we add 7 note or 6 note or 5 note melodies, allso variations in rhythm.

There is much room for new music!

Anand

anand, being a physicist myself I have to correct you there 😉: the minimal number of 8-note melodies is 12^8 (taking a melody as an ordered set with repetitions - see guy’s first masterpiece 😃), which is already nearly half a billion. as you point out this does not take into account that notes can have different lengths … as well as different velocities, being played with different articulations, dynamics, vibrato—and changing some of these additional properties you can easily mess up any good melody.

so the odds to find a good melody by chance should be far less than hitting the jackpot. but the amazing examples in this thread (which I enjoyed very much!) show that music is not math and that all these extremely talented people here definitively know what they are doing 😊.

Hi Kai

I had stated that my calculation assumed no repetitions. You are right that it is 12^8 (or roughly 1 billion) with repetitions, which makes sense. But I like to exclude repetitions since a melody like  C C C C C C C C is obviously not interesting. And this is for only one note length and I never intended to include any variations in expression and articulation or dynamics. One could go crazy with this calculation and I am not that interested. This was just for a rough idea. 

I did not intend to suggest that music is math (oh please, lets not get side tracked here!) but posted that with the idea that someone might be curious about the number of combinations possible. 

The traditions of classical music composition have found ways to teach us how to narrow down this amazingly complex "landscape" of tonal possibilities into beautiful melodies without ever knowing math. It is fascinating to me that a computer algorithm that churns out melodies will probably take a million years to write a melody like Tchaikovsky or Mozart that can move us emotionally. How does the human brain achieve it? Fascinating.

Cheers

Anand

Re: Passages, Thank you Paul, William, and Anand for your kind words. It slipped my mind to mention, it's actually alto clarinet, along with harp and accordion...making it even more unique instrumentation, as the alto rarely is heard in this context. Yes, Jos, Becky and I played the piece live with harpist, Erica Goodman, and then changed in to our wedding outfits, and the stage went from a concert stage to a wedding chapel :) I agree that the musical mood of the piece doesn't necessarily match the joy of a wedding, but I wanted to write something richly romantic and dramatic. Cheers! Dave

Congratulations to everyone participating in this (great thread Bill), and thanks for the kind words Anand and good work too. Since people started posting what they refer to as their good stuff, I thought I'd put up something I wrote in this century. It has been interesting for me to monitor people's musical backgrounds and interests through this exercise. It seems that most listen to film music primarily (a lot of music offered here screams this), and less to the classical tradition (by 'classical' I mean anything 800-1950 A.D.). I'd just like to say guys, that as much as I too love film music and I marvel at the great tracks this genre's masters have offered us, the real wealth lies in the other direction. If you wish to enrich your musical vocabulary significantly and listen to the best melodies that have ever been conceived, take a break from film for a while, shift the balance a bit. Just a suggestion.

https://soundcloud.com/errikos-vaios/wings

@Errikos said:

Congratulations to everyone participating in this (great thread Bill), and thanks for the kind words Anand and good work too. Since people started posting what they refer to as their good stuff, I thought I'd put up something I wrote in this century. It has been interesting for me to monitor people's musical backgrounds and interests through this exercise. It seems that most listen to film music primarily (a lot of music offered here screams this), and less to the classical tradition (by 'classical' I mean anything 800-1950 A.D.). I'd just like to say guys, that as much as I too love film music and I marvel at the great tracks this genre's masters have offered us, the real wealth lies in the other direction. If you wish to enrich your musical vocabulary significantly and listen to the best melodies that have ever been conceived, take a break from film for a while, shift the balance a bit. Just a suggestion.

https://soundcloud.com/errikos-vaios/wings

What a stunning piece and performance. I'll keep it as my goal to transcribe this piece as an exercise.

I can't express how thankful I am to this forum....to be able to hear amazing music like this and to actually communicate with the composers.

Anand

PS btw I focus mostly on classical music while listening, much less on film.

[/quote]

"But I like to exclude repetitions since a melody like  C C C C C C C C is obviously not interesting." 

[/quote]

Tell this to Terry Riley by the way 😉

Thanks a lot Guy I appreciate it!   Your brilliant composition and performance are an inspiration. 

Also, the pieces by Jos, Paul and Anand are very fine.  Not to mention the others here - all very interesting and worthwhile music.  Errikos, that is a great song.  I need to listen more - complex and fascinating work.

 

Hey!  This thread has become friendly and cordial !  What's up with that?  I'm getting nervous.

@agitato said:

Hi Kai

I had stated that my calculation assumed no repetitions. You are right that it is 12^8 (or roughly 1 billion) with repetitions, which makes sense. But I like to exclude repetitions since a melody like  C C C C C C C C is obviously not interesting. And this is for only one note length and I never intended to include any variations in expression and articulation or dynamics. One could go crazy with this calculation and I am not that interested. This was just for a rough idea. 

I did not intend to suggest that music is math (oh please, lets not get side tracked here!) but posted that with the idea that someone might be curious about the number of combinations possible. 

The traditions of classical music composition have found ways to teach us how to narrow down this amazingly complex "landscape" of tonal possibilities into beautiful melodies without ever knowing math. It is fascinating to me that a computer algorithm that churns out melodies will probably take a million years to write a melody like Tchaikovsky or Mozart that can move us emotionally. How does the human brain achieve it? Fascinating.

Cheers

Anand

 

hi anand,

so sorry, i missed that you made this assumption. in this case my point is not about the math, but rather about the assumption itself, because you should have a hard time naming a famous melody without a single note repetition.

my post wasn’t entirely serious and i did not want to turn this into a nerdy discussion about math 😊, i was just surprised to read such a post on this forum. 

my main concern is your assumption that every 100th melody is “good” (which is surely hard to define in first place). i would guess that out of the nearly uncountably many (landscape is a good picture), the percentage of melodies that a large number of people agrees on to be “good” is FAR smaller. otherwise we would hear many more of them … and that’s why the exquisite examples in this thread are so special.

i fully agree with your statement about classical music, but i am not sure about the million years. neural networks are making tremendous progress. recently the same architecture of the “alphago” software that had previously beaten the world champion in the game of go taught itself in less than a day how to play chess (and other games) and plays now better than specialized chess software (despite decades of development of the latter). the “deepdream” networks can already “imitate” famous painters and the results are quite stunning (although a bit creepy). so i wouldn’t be surprised if a neural network would learn how to copy a certain style and “compose” e.g. “tchaikovsky-esque” music in the next decade. coming up with really new ideas is surely much harder, but who knows, maybe a neural network can one day even learn what makes a melody great and implicitly apply this complex recipe (which likely won’t consist of a few simple rules) to come up with new ones …

cheers

kai