Overtone Music Network

a common space & database for harmonic overtones

There are literally hundreds of ways to tune an instrument by dividing the octave circle in twelve halftones. But whether your tuning system is 'equal tempered', 'just', 'mean tone' or one of the many 'well tempered' tunings, the pattern behind the division of the octave in twelve halftone steps, the universal structure, derives from combining the two major forces in music:
- The octave as the frame of all musical scales, the 'identity interval', ratio 1:2,
- The perfect fifth as the 'generator interval', ratio 2:3.
In the animation the octave covers one winding of a spiral, so in this perfect analogy between aural and visual presentation you return to the same quality on a new level.
The perfect fifth covers 210.6 degrees.

The issue here is NOT to advocate Pythagorean tuning but to illustrate how this universal pattern behind all tonal systems is created.
Furthermore this will shed light upon the contractive and expansive forces of musical intervals which govern all harmonic and melodic dynamics in music.
An interval tends to resolve its tensions either outwardly (generally major and augmented intervals) or inwardly (generally minor and diminished intervals).
As it may be clarified from the animation, the 12 halftones generated by 12 perfect fifths are not evenly distributed in the octave circle -- the generation principle gives birth to 'minor' halftones (dia-) and 'major' halftones (dia+), so not only the 7-tonality is diatonic, but the 12-tonality from its root may be considered diatonic as well.
This diatonic trait may reveal that the breakdown of tonality in early 20th century could just as well have been considered an invitation to new opportunities with a wider frame of tonality -- so far this invitation has been left virtually unanswered.

The animations of both the 7-tonality and the 12-tonality have three stages:
- Generation by sequence of perfect fifths:
7-tonality: 00:00, 12-tonality: 02:00
- Octavation:
7-tonality: 00:58, 12-tonality: 03:20
- Scale:
7-tonality: 01:44, 12-tonality: 04:40

The piano sounds of the animation are tuned to Pythagorean tuning.

D has been chosen as central note for the sake of symmetry.

More to be found (in danish) at Knud Brant Nielsens website http://www.tolvtonalitet.dk

This content has been seen 72 times

Comment

You need to be a member of OMN to add comments. Sign up, it's free!

Join Overtone Music Network

Sponsored by:

Latest Activity

Joel M is now in contact with Harmonic Introductions
Sunday
NamasteMusic posted a video

NAM: "Before I lay down in grief" [Official Video | HD]

NAM: "Before I lay down in grief" (OFFICIAL VIDEO) from the new album "Schattenbilder" NamasteMusic 2015. Download: https://itunes.apple.com/us/album/schatte...
Friday
NamasteMusic posted a photo

NAM-Album Rezension Sonic Seducer 07/2015

NAM-Album Rezension Sonic Seducer 07/2015Order @ iTUNES:…
Friday
Erik Om posted an event

Meditative concert with sacred instruments Bloue moon" in Barcelona at Center "elements"

July 31, 2015 from 8:30pm to 9:30pm
A meditative concert to celebrate the blue moon, second full moon in the same month Erik Om Maribel…See More
Thursday
Leonoor is now a member of OMN ...

Welcome Leonoor!
Jul 22
Jens Mügge commented on the event 'Sound and Healing Celebration 2015'
"Wie war's?"
Jul 21
Skye Løfvander updated their profile
Jul 17
Imre Peemot is now a member of OMN ...

Welcome Imre Peemot!
Jul 17

© 2015   sponsored by Yoga Vidya, Germany

 |  Support | Privacy  |  Terms of Service