Comments on: Music and the Fibonacci Sequence and Phi

By: Gary B Meisner

Gary B Meisner — Wed, 23 Feb 2022 02:01:28 +0000

In reply to TOLLY NONE. The number of the Fibonacci sequence that apply here are 1, 2, 3, 5, 8 and 13. The point is simply that various ratios formed from these numbers create tones of the musical scale. There is not a pattern in that per se.

By: TOLLY NONE

TOLLY NONE — Sun, 20 Feb 2022 17:05:37 +0000

Hello! Sorry, but I’m a bit confused as to how the Fibonacci ratios were derived in the table of the music frequencies. Is it just random Fibonacci numbers dividing each other in some sort of pattern? I’m trying to figure that out because the Fibonacci ratios are said to be the numbers dividing the previous number; so 1/1, then 2/1, 3/2, 5/3, etc. But the table shows 1/1, 2/1, then 2/3 instead of 3/2. Could you please elaborate on this? Thank you

By: vasily markelov

vasily markelov — Mon, 09 Nov 2020 22:19:14 +0000

In reply to Fab. anybody analyzed chapels ratios in other galaxies? would have been very interesting as well

By: Jeremy

Jeremy — Fri, 16 Oct 2020 07:29:16 +0000

In reply to Darwe.

I’m new to the math here – day old in fact! I just ordered a custom metal torus shape tongue drum – it’s got 9 tongues. I asked for it to be tuned to 432 hz with the golden mean / Fibonacci sequence – and with 9 tongues and the 432 this could also well connect with the 9 major chakras (still figuring it out before the smith finalizes the tuning).
I quickly learnt that’s not straight forward. With their great help as well as a web search – this was my favored landing place as I realized quickly Gary and co are right on the money here – and with help from Gary’s musical chart above as well as Darwe’s input I came up with a ‘formula’ for this – below is sort of an inverse math check (I’m not fully sure of how accurate this is and also realize Fibonacci and octaves need assistance to combine):

Relating the 9 notes mathematically to 432 hz:
C256 x 1.5 x 1.5 x 1.5 div 2 = 432
D288 x 1.5 = 432
E324 x 2 div 1.5 = 432
G384 x 1.5 x 1.5 div 2 = 432
A432 x 1 = 432
C512 x 1.5 x 1.5 x 1.5 div 2 div 2 = 432
D576 x 1.5 div 2 = 432
E648 div 1.5 = 432
G768 x 1.5 x 1.5 div 2 div 2 = 432

How does this look – does this work?
Thanks, Jeremy

By: Hjörtur Howser

Hjörtur Howser — Tue, 22 Sep 2020 22:19:21 +0000

Freddie Mercury’s glissando climax in “Under Pressure” always gives me the chills as the near perfect phi moment in a pop song. Whether or not Bowie and Mercury were aware of the “golden ratio” or if this was only a fortunate stroke of serendipity we will perhaps never know – I like to think they knew exactly what they were doing 🙂

By: john stephen agresti

john stephen agresti — Mon, 13 Jan 2020 00:04:24 +0000

In reply to Alan Ingram. I came across a brief abstract about wave formation of the drum head. It's a symmetrical formation but maybe there's some Fibonacci that accounts for the wave carrying itself out into the atmosphere?

By: Katie Anderson

Katie Anderson — Thu, 01 Aug 2019 00:19:56 +0000

Gary Meisner, thank you for the link. I am curious of the impact of the phi harmonics on human consciousness as evidenced in classical forms as well as works like Gustav Holst’s The Planets and how this differs from older performances vs instruments attuned to the 440 frequency. A friend of mine described the difference between a stradivarius and any other violin as being especially crisp and clear and I have heard the difference as well. I’m writing an essay that addresses Phi and Fibonacci in a series of ritual performances called the rites of eleusis that combined poetry, music and dance, which were performed for a limited run in the early 20th century, and are reproduced by various performance companies to this day.

By: Иван Ткаченко

Иван Ткаченко — Thu, 17 Jan 2019 11:55:12 +0000

I want to draw the attention of people interested in music and the golden section to my son’s publication, where an analysis of the hyperbolic-type wave equation is made from the positions of the golden section to determine
the frequencies of the sound of the notes of the first octave with the interval of the root of the eighth degree of the golden ratio 1.618, and not the root of the twelfth degree of 2.

I.S. Tkachenko, M.I. Tkachenko, Wave equation: Fibonacci functions, Luke functions and dynamic harmonic oscillatory process // “Academy of Trinitarianism”, M., El. 77-6567, publ. 23737, 16.09.2017

Хочу обратить внимание интересующихся музыкой и золотым сечением на мою с сыном публикацию, где сделан анализ волнового уравнения гиперболического типа с позиций золотого сечения для определения
частот звучания нот первой октавы с интервалом корень восьмой степени из золотой пропорции 1,618, а не корень двенадцатой степени из 2.

И.С. Ткаченко, М.И. Ткаченко, Волновое уравнение: функции Фибоначчи, функции Люка и динамический гармонический колебательный процесс // «Академия Тринитаризма», М., Эл № 77-6567, публ.23737, 16.09.2017

By: datkid

datkid — Wed, 02 May 2018 10:49:36 +0000

In reply to Becky. man thanks so much , i am doing a maths project and that answer goes perfect with my question. I straight away copied and pasted it

By: Gary B Meisner

Gary B Meisner — Mon, 01 Jan 2018 17:06:22 +0000

In reply to Yuri Landman.

First, the Harmony of the Spheres is an ancient philosophical concept that regards proportions in the movements of the Sun, Moon, and planets as a form of music. This “music” is not literally audible, but reflects a harmonic, mathematical or religious concept. This article and this site makes no such claims and has nothing to do with this.

Re Phi as one chapter of “Harmony of the Spheres,” one misuse of a concept does not mean that the entire concept is invalid for all other uses. This is called a Faulty Generalization fallacy:

https://en.wikipedia.org/wiki/Faulty_generalization

Also, there is nowhere on this site that I assume Phi to be ‘the truth’ in art. If you take the time to read the content here you’ll find that I and those who use it in the design arts recognize it as a valuable tool to aesthetically pleasing composition decisions. It’s not a silver bullet or a universal truth. Your assumption and statement here would be called the Jumping to Conclusions fallacy:

https://en.m.wikipedia.org/wiki/Jumping_to_conclusions

Lastly, the point of the article is not the Fibonacci sequence defines every aspect of music theory and scales. It was just a simple, fun observation that the 13 notes that comprise an octave in the key of C on a piano keyboard are broken down into sets of 8, 5, 3 and 2 keys, which are all Fibonacci numbers, and that many of the frequencies ratios that define the notes in a scale also use Fibonacci numbers, such as 3/2, 5/3 and 8/5 and others. It was really just that simple. Asserting that a relatively small first step leads to a chain of related inferences culminating in some significant conclusion is an example of the Slippery Slope fallacy.

https://en.wikipedia.org/wiki/Slippery_slope