Composing using the Golden Ratio <3 ! !! !!

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Im working on some coursework and im absolutely head over heels with the concept of the phi point. Phi is 0.6180339985218034... you'll know it as tyhe golden ratio. Its related to the fibonacci sequence by the fact that adjacent numbers in the sequence occur around this ratio. The higher up you go in the series the closer you get to that number.

The golden ratio is EVERYWHERE in nature so its inherentrly pleasing to the senses. Ive not heard anything about it appearing in acoustics (Im certain it does I may dedicate my postgrad thesis to this ) but it appears in snail shells and so and so forth.

In terms of art im working on a piece which is divided up into sections which are in the folden ratio. The melodies rhythms and harmonies are governed by the ratio. The entire piece is ruled by that number. It imparts real motivic unity to the whole and the parts and also forms a fractal sort of relationship. A fractsal is a shape which contains itself ad infinitum. So you might have a 4x4 square which has another 4x4 square inside it which in turn ahs a 4x4 square inside it and so on and so forth.

So has anyone else conducted any experiments in this field

Ahhhhhhhhhh Fascinating phenomenon

Phi points from C to B and F# to F create a whole tone scale

Last edited by binaryodes on 06 Jan 2014, 7:55 am, edited 1 time in total.

wish I could say I was that advanced cognitively, but at least I have heard of the aforementioned ratio before, and have seen it demonstrated in the faces of supermodels.

How precisely do you get from C to B and F# to F? It appears you are going a half step down, then a fifth up, but that's me being stupid--how, precisely, are you using phi?

And what do you mean by a phi point? You seem to use the phrase both as "phi point" (a noun) and "phi points" (noun + verb).

Im writing my essay now so i'll post some proofs up if you're interested. Absolutely fascinating stuff

I'll produce the proper proof as im literally just finished and need to head out to uni to print press and post my coursework buuuuut.

Map C to B and F# to F in semitones
Calculate total number of semitones
Multiply that by 0.6180339985218034
Multiply answer by 0.6180339985218034
Rinse and repeat until you get to 1
Youll have a set of numbers

Referring to your grid which should look like this

C C# D D# E
F# G G# A A#

Map the numbers along the grid (f# in this grid would be 6 not 1)

You SHOULD have the notes of a whole tone scale but this is from memory so I havent actually checked it properly


B C D E F G A B
C Db Eb F G Ab Bb C
D Eb F G Ab Bb C D
E F G Ab Bb C D E

C D E
Db Eb F
Eb F G
F G Ab



Thats one I made earlier using the same process. Its stacked locrian scales. I worked out which modes to stack by taking the phi points of b Locrian (( C D E) and using them to fill the gird. The end rectangle contains a chromatic scale!!

http://m.youtube.com/watch?v=ahXIMUkSXX0

Can someone please help me? Please take this web address (above) and make it into a direct, Youtube link. Or, better yet, please explain how I can get the Youtube icon-shortcut tool to work properly. (It's so frustrating. Every time I try to post a Youtube video-link, after I click the icon, then copy & paste the Youtube web-address into the little, white Youtube icon-web-address box, it, unfortunately, only makes the following, unlinkable web-address appear...like this:

[youtube]http://m.youtube.com/watch?v=ahXIMUkSXX0[/youtube]



I've noticed that others on this site haven't figured this "link trick" out, either. (This link would really help add to the OPs discussion. Just tryin' to help!)

A little help here, please. Thanks

[Mod. edit: the links fail to show as embedded videos because you're pasting a YouTube URL intended for use on a mobile device.
It's not the content causing the problem - it's the way the URL is formatted to use "m.youtube". The site software will only recognise and correctly display a YouTube URL if it starts with "http://youtube.com".
Note that using a URL starting with "https" will also fail (and this applies when linking static images too).
Here's the same URL you posted above, edited to a non-mobile device form]

[youtube]http://www.youtube.com/watch?v=ahXIMUkSXX0[/youtube]

Last edited by WilFindUndrstndng on 09 Jan 2014, 6:28 pm, edited 1 time in total.

Ok, so...that first link worked(!), however, all I did (to get it to work) was NOT use the little "Youtube" icon. I just copied the address into the text. But, why won't the icon thingy work? If it DID work, I'd just see a big video screen with a "play" button in the middle, right?

Why does this hafta be so confusing? Is this strictly an iPhone problem?
[Mod. edit: yes - or rather, it's a mobile device problem in that the URL form most suitable for those devices tends to be used which, when copy/pasted here, will fail because the forum software doesn't understand it]

ANYWAY, THE VIDEO-LINK (in my post above) IS WAY-AWESOME.

Thx!

Golden ratio in music usually refers to form. Start with a small motive, build that into a phrase, phrases into large sections, and larger contrasting sections into entire movements. All that is often loosely based on the GR for proportion sake.

Acoustically, I can't imagine you'd have much use for it. I suppose you could use the GR to determine musical intervals such that you could create different spectral effects, which might be interesting.

You could also do some interesting things with additive synthesis and frequency modulation. Here's a bell sound I created using 0.6180 as a harmonic coefficient. There are three tones. The first uses 0.618 as a FM modulator ratio with the carrier ratio of 1. The second reverses the ratio to 1:0.618. The third has both sine waves going directly out, no modulation, at equal amplitudes.

http://soundcloud.com/angelrho/golden-mean-experiment

Phi is derived by adding 1 to the square root of 5, and then dividing the result by 2. This yields:

Phi = 1.6180339887498948482045868343656

The ratio between any two adjacent notes (half-step separation) in the Equally-Tempered Chromatic Scale is exactly the twelfth root of 2 (which is 1.0594630943592952645618252949463) -- NOT Phi.

Thus, while A-Natural is defined as 440 cycles per second, A-Sharp is 466.1638 cycles per second, when rounded off to seven digits. Thus:

A = 440.0000 cycles per second
A#/Bb = 466.1638 cycles per second
B = 493.8833 cycles per second
C = 523.2511 cycles per second
C# / Db = 554.3653 cycles per second
D = 587.3295 cycles per second
D# / Eb = 622.2540 cycles per second
E = 659.2551 cycles per second
F = 698.4565 cycles per second
F# / Gb = 739.9888 cycles per second
G = 783.9909 cycles per second
G# / Ab = 830.6094 cycles per second
A = 880.0000 cycles per second

Multiplying 'A' by Phi yields 711.9350 cycles per second, which does not match any other note on the scale. Continuing this process with any other note on the scales yields no other note on the scale.

I know that there is a lot of 'mysticism' related to the Golden Ratio, Pythagorean Musical Ratios, and the alleged "Harmony of the Spheres", but when you crank the numbers, these 'mystical' relationships just do not add up.

You misunderstand me. My composition was for piano so I wasnt dealing with cycles per second at all. I havent even begun to explore the potential for precise ordering. In fact I never considereed constructing a scale based on the cycles per second. Im also not aware of any real mysticism and I just found the "trick" an amusing process

The Equally-Tempered Chromatic Scale is used on pianos and other 'keyboard' instruments.

Cycles-per-Second is how the pitch (e.g. frequency) is measured.

Does my post suggest otherwise ???


Edit: I see where the confusion is coming from. What I mean is that on the piano you dont think in terms of cycles per second you think in terms of discrete notes as oposed to a continuum. Its thinking tonally instead of rhythmically in a weird sort of way - not that theres any real distinction.

A phi scale would have a compass (X cycles) which you subdivide into different parts in the ratio of phi. What ive been doing is a loose approximation of this using the coarse measuring system of the keyboard

Yes.


I am an engineer. I think in engineering terms. Pitch is frequency. I am also a musician. "A Above Middle C" is 440 cycles per second, exactly. Any value other than this is not "A Above Middle C". Middle C is ~261.6256 cycles per second (or exactly 261.6255653005986346778499935233 cps) on any chromatically-tuned keyboard instrument. A keyboard instrument tuned to the Pythagorean or Phi scales sounds horrible.


The Phi scale does not fit in a keyboard-generated scale. A keyboard does not have a coarse measuring system. A keyboard has a precise tone-generation system. If the notes are not related to each other by the chromatic interval, then the instrument is out of tune. The Phi scale is imprecise. Therefore, the Phi scale is useful only for out-of-tune pianos and electric guitars.

"Compass" and "X cycles" are not musical terms.

You do know that humans tune pianos. Theres nothing EXACT about it at all. Theres going to be variance of a few cents at the very least. You're also thinking in incredibly prescrptive ways. I had a housemate who recognised this in me as well and ive worked on it. I also never suggested tuning a keyboard to the phi scales. Furthermore it sounds horrible to YOU. If you're talking about midi keyboards then yes 261. ...... is accurate. On a hand tuned piano forget it. I imagine that you have perfect pitch.



Measuring systems go from fine to coarse. A fine measuring system would be tiny intervallic distances. C to C# keys would be a few cents in difference. We'd have to multiply the number of keys by a factor of over 50.
TYhe problem we have here is that you're insisting that "this is the way it MUST be. There can be no other way". If we lived in the 17th century or we were sitting with Bach poring over das wohltempierte clavier your arguments would carry weight. As it is there are a vast array of experimental ways to tune a keyboard. It can only be out of tune in relation to a universal constant written in the cosmic ledger. There is on such thing. We invented the tuning systems and deviance constitutes another invention equally valid.

How is the phi scale imprecise????

X cycles = x AMOUNT of cycles
Compass - range

Who cares if theyre not musical terms. I know this is a forum for aspies and theres a lot of cognitive rigidity about but "These arent musical terms" is over the top even here. Are you suggesting that we stop inventing new musical terms. Specify a date from which all further musical coinage becomes incorrect.

I cant figure out WTF he's talking about either.

OP: are you talking about compositional form (perhaps lengths of melodic passages calibrated to the Golden Ratio)?

Or are you talking about musical tones themselves being created by somehow using the golden ratio?

If its the former (form) then presumably you would just be using the traditional Western musical scale to play around with composition.

But if its the latter then you would in effect be inventing a whole new musical scale to replace the traditional Western musical scale by creating a new set of notes from pitches dictated by the golden ratio.

In that case you would be using notes that sound out of tune to Westerners to make whole out-of-tune compositions. Concievably these strange tones might work together (kinda like Indian Raga music, or Chinese music, works even though each note is foriegn to the western scale-they work together in the same piece- sometimes even to Western ears).

I suspect that you dont understand that a 'note' is a specific pitch. A pitch is a specific number of vibrations per second. The note A about middle C is 440 vibrations per second- regardless of what instrument its played on. If you mulitply that by 1.62 you get a pitch thats not on the normal musical scale. And if you mulitply THAT by the golden ratio you get another non-existant (or non conventional) 'note'. And so on.

I find this post vaguely offensive particularly the last part. When I indicated that pitches are rhythmic I made it clear that I understand that a tone is a wave and pitch is determined by vibrations per second.

I thought that I was clear but I dont think that either of you understand the basic principle.

My coursework brief was to compose a piano piece using one of several musical devices. I used golden ratio amongst other things. In the context of a piano piece the only way to create ordering at the level of pitches etc was to number each note of the scale. C D E F G would be 1 2 3 4 5.