Scorpio

I'm still learning to use the orchestra, but I can't write things in classic forms.... So, taking Bartók as  a model for the Form, I used the Fibonacci series. This is in the notes of the score:

I really don't know what happened there, but I loved it! That single resolution to the tonic at the end was so satisfying after all the tonal trip. 

6 minutes ago, JorgeDavid said:

I really don't know what happened there, but I loved it! That single resolution to the tonic at the end was so satisfying after all the tonal trip. 

 

Thanks!

You have to dive into Bertók a little... But the Axis System is an extended tonality way to work. That is to say: it is tonal, but each area (tonic, subdominant, dominant) involves 8 tonalities (for example tonic area includes C, Cm, F#, F#m, A, Am, E, Eb... From one tonality: the augmented 4th, and the mediants by minor third...., and all their relative minor ones).

On the other hand the Fibonacci series is used as the moments where there is some change, in this case the area changes. This a way of contemporary Form, used by Bartok, Debussy, and others...

Additionally, I created a scale from the Fibonacci series. Bartok created some chords using the Fibonacci series, too.

Actually, one of my future plans is to dwell into the music of Bartok and its compositional system because I heard it is also the basis of much of what the greats of Jazz, such as Chick Corea or Miles Davis, composed. I find mesmerizing most of the content of the Mikrokosmos volumes and the counterpoint used there. Thank you for the explanation and the nice music! I will surely try to get into all this in the future when I feel ready for it!

Where you portray the axis system for this piece I notice that it says that the Sub-Dominant for Eb is D so I'm assuming you meant that to be Ab which is on the opposite side of the circle?  I like the unique combination of consonance and dissonance that you manage here.  I noticed that the scale which you derived from the Fibbonaci series here (great idea btw) can be thought of as a penta-chord that is then transposed to the dominant level.  C Db D Eb F (0, 1, 2, 3, 5) transposes to G Ab A Bb C which is neat.

Great result in the music!  I am not sure whether all the golden ratios scattered throughout this composition are really detectable to the ear but it's a neat way to plan out the composition.  What I would be stoked about is if a golden ratio snuck into one of your compositions even if it was un-planned.  I really liked the build-up to and the ending itself.  I loved the last C6 chord.  Nice job!

Tonic, subdominant, and dominant are areas of tonalities, and you can change one for another without changing the function. It is not that one chord is whatever for another chord, specifically. 
 

Using the fibonacci series and the golden ratio is a Form. Many composers worked with it.

8 hours ago, Luis Hernández said:

Using the fibonacci series and the golden ratio is a Form. Many composers worked with it.

I know that Bartok, in his Music for Strings, Percussion and Celesta 1st movement has the climax at the golden mean, but I doubt that he did that deliberately as a formal plan.  It was only later, after it was composed that some theorist analyzed it and found that it conformed to the golden mean in its structure.  Who are these "many composers" who worked with it?

44 minutes ago, PaperComposer said:

  Who are these "many composers" who worked with it?

 Mozart sonata 1 in C maj

 Beethoven 5 Symphony Mov I

                     Piano sonata  14

Debussy Claude Debussy’s Dialogue du vent et de la mer

                 Cloches a travers les feuilles 

Erik Satie and the Sonneries de la Rose+Croix

Bach  the art if fugue

Chopin prelude in A minor

Haendel Messiah 

Etc

I'm sure that those compositions have many interesting characteristics some of which may in fact be formal units divided according to the golden ratio, but I highly doubt that Beethoven, Mozart, Debussy, Satie, Bach, Chopin or Handel planned out their compositions in the way that you did with this piece.  I'm not saying you shouldn't do it that way or that it is somehow 'bad' but I'm pretty sure they just composed intuitively and some theorist later analyzed their pieces and noticed the golden ratio in their works.  In other works they did it unintentionally which is that much more impressive (imo).

Perhaps. But some times it was totally planned as Bartok or a Debussy did.

6 hours ago, PaperComposer said:

I know that Bartok, in his Music for Strings, Percussion and Celesta 1st movement has the climax at the golden mean, but I doubt that he did that deliberately as a formal plan. 

Look! This can't be done by chance. It's all planned. The movement is a big fugue where tonalities, dynamics, etc..., they all change in the measures that correspond to the fibonacci series.

On the other hand, this series and ratio is known long long ago and was used by all kind of artists. I'm not surprised that composers that loved mathematics and nature used this stuff in their compositions.

1 hour ago, Luis Hernández said:

I'm not surprised that composers that loved mathematics and nature used this stuff in their compositions.

I think that even if they didn't like math or nature they would end up using it just through cultural osmosis. It's hard to escape those kind of pervasive aesthetic paradigms.

6 hours ago, Luis Hernández said:

Look! This can't be done by chance. It's all planned. The movement is a big fugue where tonalities, dynamics, etc..., they all change in the measures that correspond to the fibonacci series.

I searched for "Bartok Golden Ratio" and found a source which talks about this subject.  The name of the theorist who posited that there was a relation between Bartoks MSPC mvmt. 1 and the Fibonnaci sequence was Erno Lendvai and this pdf actually states later on that the MSPC mvmt. 1 is more akin to the lucas numbers (closely affiliated with) rather than the Fibonnaci numbers.  It also states that those sequences are nowhere present in his manuscripts.

Bela Bartok and the Golden Section

19 minutes ago, PaperComposer said:

It also states that those sequences are nowhere present in his manuscripts.

I know about that and Lendvai.

Bartók didn't write anything about his methods in composition. That doesn't mean he didn't have. Many composers didn't write about their methods, and some were revolutionary (Wagner).

But you are free to believe what you want, or course. However, if this Bartók's piece is how it is by chance... what kind of Form is it? ¿None? It's not important if it follows the fibonacci series or the Lucas one; the question is if he followed any of them.

In the 20th century many new Forms were created, some of them based on irrational numbers and its series (fibonacci, pi, e, etc...) some based on other concepts (rhytmic boxes invented by Cage, mosaic forms, and later indeterminacy, etc...).

3 minutes ago, Luis Hernández said:

However, if this Bartók's piece is how it is by chance... what kind of Form is it?

I think he did intend a deliberate form and that was the wedge form which you so conveniently pictured above in your post.  It's a fugue in which every successive statement of the subject gets farther and farther away from the original key through the circle of 5ths in both directions, until at the end of the piece it returns to A.  I think he un-deliberately created those golden sections in his work because after the climax he abbreviated the denouement and return to the original key through heavy use of stretto.

35 minutes ago, PaperComposer said:

he un-deliberately created those golden sections

Too many coincidences, I think. But we will never know what Bartók had in his mind.

But he has more works that follow this series (or there are coincidences, too.

1 minute ago, Luis Hernández said:

Too many coincidences, I think. But we will never know what Bartók had in his mind.

But he has more works that follow this series (or there are coincidences, too.

I think the fact that these sequences appear in composers and other artists compositions is a testament to the fact that nature speaks through us when we pursue beauty in art.  To me it just means we are part of nature.  I think it would be putting the cart before the horse to say that all these compositions were planned to have the golden ratio in them.  Yet they aren't exactly coincidences either - they are just features of nature and beauty and grace.

What other Bartok works had the golden ratio?

6 minutes ago, PaperComposer said:

What other Bartok works had the golden ratio?

Look for it! I'm tired of this, I have nothing to prove. You can understand this music as you like.

3 minutes ago, Luis Hernández said:

Look for it! I'm tired of this, I have nothing to prove. You can understand this music as you like.

Sorry .. I thought we were just having a friendly discussion /-:  My apologies

14 hours ago, PaperComposer said:

Sorry .. I thought we were just having a friendly discussion /-:  My apologies

No I'm sorry, instead.

But this is as if told you Haydn didn't thought about the Sonata Form and went to it by chance....

Debussy also used the golden ratio

Other:

In 1907, Kodály writes Méditation sur un motif de Claude Debussy. Just as with the fugue from Bartók’s Music for Strings, Percussion and Celesta, the piece opens pp and ends ppp, with a central climax marked fff. If one counts quarter notes rather than measures, there are 508 beats. The golden ratio of 508 is 314 (to the nearest integer) and this just happens to be smack in the middle of the two climatic bars at fff.

Third mov of Music for strings, percussion, and celesta

Other works by Bartók where the golden ratio can be detected are Sonata for Two Pianos and Percussion, Miraculous Mandarin, and Divertimento.

Bartók was highly secretive about his works. Surviving manuscripts of many of the pieces where the golden ratio appears to have been used contain no mention of it. Bartók was already being criticized for being too “cerebral” in his music. Identifying the mathematical patterns in structure and tonality (even to his students!) would have only added fuel to the fire. G. Roberts (Holy Cross)

I listened to it without delving into the analytic commentary which would probably bias my reception. For example, the mention of Bartok led me to wonder if it would have hints of Bartok. It has only the slightest hints.

I'm none too familiar with Bartok's oeuvre except his string quartets and a few orchestral works and aside from the quartets, just at the listening level. So however the analysis worked it didn't remind me of anything Bartok I know.

It's an accomplished work, interestingly scored and with tempi variations, motivic (to me) rather than long thematic lines...I'll need to listen to it again to affirm my thoughts or otherwise.

No matter, an enjoyable listen all the same.

Congratulations. 

Wow!
What a wild ride.
 

I am not too familiar with the works of bartok: the latest composer I can claim any intimate knowledge of beyond mere listening is Wagner.

But I loved this, the resolution at the end feels so sattisfying and while the harmonic complexity of this piece is quite sophisticated it feels so "uncontrived", so natural. The textures, rhythm variety, the unexpected pleasantness (usually when pieces have highly theoretical motivations they sound rather noisy to my ears). Really great! Well done.

5 hours ago, Quinn said:

the mention of Bartok led me to wonder if it would have hints of Bartok. It has only the slightest hints.

Thanks for listening.

in fact, I was not trying to sound like Bartók..., I would love to... I only wanted to use some of his methods.

@bdk  Thanks also for your time. As you mentioned Wagner..., in this piece Siegfried leit motiv appear twice, but hidden between other countermelodies...

You know it's going to be good when the description and half the comments have some form of diagram in them.

Well composed, Luis!