Cracking the Code

[Pierrot]

Originally Posted by GregorArturo

If anyone can help with the most appropriate scale it would be greatly appreciated. I am using five-limit just intonation which is based on the primes 2, 3, & 5. My previous scale was most related to "pythagorean tuning" and was based on the primes of 2 & 3 only.

I'm reading through this article at the moment: http://en.wikipedia.org/wiki/Just_intonation

So much can be said on this topic ;-)

I'd recommend an excellent book of Ron Gorow "Hearing & Writing Music" - "The natural harmonic curve is evident in shells and even the cochlea of the ear. It is a proportion of innate aesthetic beauty, present in many forms of art from antiquity to the present.(...) Harmonic rhtyhm has been revealed in the periodic table of elements and intervals of electron shells within an atom - the very essence of matter and energy. All things in our physical world, from the subatomic to the cosmic, reflect or produce a rhythm of harmonic proportion. That includes every musical tone."

In order to understand what's a musical tone have a look at the Harmonics Series http://en.wikipedia.org/wiki/Harmonic_series_(music) This gives us the harmonics produced when a string vibrates, or when wind blows in a cave, etc. The Sound of Nature.

Some observations - the 2d Octave gives us the Fundamental Note-its perfect Fifth-its Octave, like in C G C (called also a "Power Chord", as used by Heavy/Metal bands, with impingement, lol) This sequence, 1 and its 5th, repeated, leads us into the Cycle of Fifths. Little note - from C to G we have a Fifth, from G to C a Fourth. But piling up Fifths gives us C-G, G-D.... and that D, being above C, gives us the One Tone interval "C to D", and dividing one octave by that one whole-tone interval we get the 12-tone scale. Btw - Ron Gorow again: "The natural scale is ideal for music that stays on one tonality (Eastern-type music). However, the beautiful proportional curve of the harmonic series refused to fit the linear system of 12 keys. (...) Pythagoras knew that the system was not mathematically perfect: 12 fifths are slightly larger (sharper) than 7 octaves". - would that account for the fact the Universe is always expanding? lol.

Back to the Harmonics Series - in the 3rd octave we find a Bb, 7th harmonic. Probably to balance out the D, 9th harmonic, Bb and D being one whole step below/above the C 8th harmonic. Nature's symmetry...

The 4th Octave gives us a sequence which approximates the Overtone Scale (also known as Lydian b7 mode, Lydian= 4th degree of a scale, b7 as the sequence is derived from the Melodic Minor Scale) Anyway - the important thing, when you look at the chapter "Harmonics and tuning" on http://en.wikipedia.org/wiki/Harmonic_series_(music) you'll notice the 10th, 11th and 14th harmonics are slightly below the notes from the equal-tempered scale. In C we would have C, ~Eb, ~Gb, ~Bb, C - which are actually the Blue Notes played in Blues. On a guitar one has to bend those notes for approximation to produce that peculiar feeling of Blues. One could also say the Octave is divided in 5 notes instead of 12, which gives notes off the equal-tempered scale. Rejecting the 12-tone equal temperement while working in the cotton fields - That freedom when playing Blues :-)))

http://www.sengpielaudio.com/calculator-harmonics.htm gives a calculator to find out harmonics, might be of help. And http://www.kylegann.com/Octave.html "Anatomy of an Octave" might be also of interest, many Mathematicians tampered with the problem at hand.

I like this thread, although mainly from the Musical perspective, but not limited to that. From Ron Gorow's book again: "(...) All objects and sounds that we are able to perceive with eyes and ears come to us in the form of waves of energy. (...) The difference between something we see and something we hear is merely a difference in frequency (...) Human perception of pitch spans from approximatively 20 Hz (Hertz or cycles per second) to 38.000 Hz (...) Below the range of human audibility, the earth vibrates at approximatively 8 Hz (the Schumann resonance) Perhaps not coincidentally, the human body in a relaxed state resonates at the same frequency, as do alpha brain waves (...) Our most intimate measurement of rhythm, the human heart, may beat less than 1Hz at rest (...) Descending the scale, frequencies become cyclic events: minutes, hours, days, years, centuries - all periodic rhythms, the stuff sound is made of. The cyclical events of nature - biological, geological, stellar - may be measured against a time continuum."

One can thus plot those waves of energy on scales, be it for colors, emotions, attitudes, .... any expression of Life, actually.

Rhythm and the pulse of the Universe, as expressed via Music. Rhythm again that enables us to tune into each other's pulse and Universe, and thus share the Present Time moment, otherwise impossible. But that would be another subject, lol!

Originally Posted by GregorArturo

EDIT NOTE: Look at the second/latter Indian scale on the Wiki article. It's based on 22 notes which essentially looks like it merges the notation systems together including all of the ratios! I'm gonna have to play around with this a little.

I love Indian Music! Very pertaining to the subject of this thread. In Indian tradition sound is God - Nada Brahma. The musician hits the chakras, awakens the kundalini, matching the being's inner sound.

Ravi Shankar in "My Music, My Life" writes about Masters of Indian music that could set fire, levitate, make flowers blossom by playing music only - Indian tradition.

Pierrot