The Octave Spiral - Overtone Visualization

Comment by Harry Smit on February 24, 2016 at 9:54am

First, a very special visualisation of the overtonescale! But I don't understand completely what is the meaning. When I Click on the question mark, ther are only 2 out of ten explanation signs. Can you tell me how I can see the other 8. Thank you so far! Harry Smit

Comment by M. L. Giannotta on February 24, 2016 at 11:35am

When you are at the second step, you need to click to the middle circle to proceed.

Comment by Skye Løfvander on February 24, 2016 at 12:36pm

Your questions are very welcome, so feel free to ask about anything which is unclear - it may also help us improving the presentation!
Further explanation:
Each of the circles represent a partial tone of the harmonic series: The one in the center is the first partial, also known as the fundamental. By following the spiral outwardly, the partials 2, 3, 4, ... etc. follow. So their frequencies will be multiples of the fundamental frequency. The last partial in this representation is 16 which is four octaves above the fundamental.
1-2-4-8-16-... represent octaves of the fundamental (at the 12 o' clock position)
3-6-12- ... represent octaves of the perfect fifth (at 210.6 degrees of the circle)
5-10- ... represent octave of the just major third (at 115.9 degrees of the circle)

Comment by Skye Løfvander on February 24, 2016 at 12:51pm

The structure of the circles are visualizations of factorization.
As you may understand from what I wrote above
- the digit 2 represents the octave (doubling and halving)
- the digit 3 represents the perfect fifth (division by three)
- the digit 5 represents the just major third (division by five)
... and all following prime numbers introduce a new musical function to the harmonic series.
The prime numbers as you can see all have a number of spokes meeting in the middle.
Apart from those there are composites of which I will use partial 15 (the second last) as an example:
It consists of two rings which means that it is composed from two prime numbers: 3 (the three division in the core) and 5 (the further division in the outer ring).
Test if the maths also makes sense musically:
3x5=15. Partial 15 is a major seventh and is composed by two steps: a perfect fifth (3) and a just major third (5) - the two intervals together (adding intervals is like multiplicating ratios) give us the major seventh.

Comment by Leonoor on February 24, 2016 at 2:01pm

Thanks Marco, you can hear that half and whole secunds are equal in the last overtones, so we have to choose what name it get. My violin teachr at the conservaory in Amsterdam in the Netherlands, died last month at the age of 90. He and his wife played violin duets with 32 tones in an octave. I cannot like the sound electronic soynd, but is is nice to see the 16 overtones and there equal steps at the end. We the living group Contact & muziek sing every day music I composed with natural hatmonies. We sing 8 years and it become mo=re and more in tune. The overtones are coming, that sounds very well. I was a violinist and overtones are very important for tuning and listening if you are playing in tune. Also children like it to hear this. So I daily work with naturally overtones, I like them very much. I want to send a recordng at home, but it seesm not possible, with love Leonoor

Comment by Luca Recupero on February 24, 2016 at 10:34pm

This visualization of overtone scale is really fantastic.
Thank you so much!!!

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