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 68 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

Harmonic Introductions posted an event

Overtone Singing Concert: An Evening of Music and Meditation at St. John's Episcopal Church

January 16, 2015 from 7:30pm to 9pm
Harmonic Introductions is holding our first public concert! It will feature original compositions,…See More
Wednesday
Indro Roy-Chowdhury is now a member of OMN ...

Welcome Indro Roy-Chowdhury!
Monday
Willi Grimm posted an event
Thumbnail

NATURTON - Hörst Du den Berg? Das letzte Konzert at UPtown Gurtenpark

December 21, 2014 from 5pm to 6:30pm
Die Reihe "Hörst Du den Berg" wird nach drei Jahren in eine künstlerische Pause eintreten und so…See More
Dec 8
Tanja Elena Quirici is now a member of OMN ...

Welcome Tanja Elena Quirici!
Dec 7
Johanni Curtet posted an event
Thumbnail

Höömij Workshop in Toulouse! at Les Ateliers d'Eau Vive

February 14, 2015 at 2pm to February 15, 2015 at 5pm
Stage d'initiation au höömij (chant diphonique mongol)Avec Johanni CurtetSaviez-vous que tout le…See More
Dec 6
A video by Barbara Lübben was featured

dat du min leevsten büst - Lauschrausch 2014

priv. Mitschnitt aus dem Obertonfestival Lauschrausch 2014 in der Yenidze, Dresden Anna Maria Hefele (Harfe) Barbara Lübben (voc) Stefan Weyh (Harfe) Jan Heinke (voc
Dec 5
Danibal posted a video
Dec 3
Elliot Witheart is now a member of OMN ...

Welcome Elliot Witheart!
Dec 2

© 2014   sponsored by Yoga Vidya, Germany

 |  Support | Privacy  |  Terms of Service