Overtone Music Network

a common space & database for harmonic overtones

# Music by numbers

Music incarnates through numbers as frequency and wawelength (= time & space) proportions of the harmonic series.

Until european renaissance most tonal system where established through combination of the first tree primes 2, 3 and 5 which express themselves as the music of the harmonic series as octave (proportion 1:2, one-to-two), perfect fifth (2:3) and just major third (4:5).

Initially this creation happens within the frame of the octave 30:60 (2x3x5 : 2x2x3x5).

The interval names of the tonal systems with frequency ratios of the form 2nx3nx5n : 2nx3nx5n

may be found on this link!

By the way the product of the following tree primes 7, 11 and 13 is 1,001!!

At the illustration the neighbouring elements placed along the axises are octaves, proportion 1:2. For example 1:2:4:.. (octaves of the fundamental/ primary tone), 3:6:12:... (octaves of perfect fifth) and 5:10:20:... (octaves of just major third).

Lesser diesis is the difference between three successive just major thirds (5/4)3 (= 125/64 = 1.953125) and the octave (2:1).

The syntonic comma is the difference between just major third, 80 (=24 x 5) and the pythagorean (generated by perfect fifths) major third, 34.

The values of the pythagorean comma and greater diesis, 73:74 and 27:28 respectively, are approximations, because their constituent values are situated further out in the branches of the spiral. The pythagorean comma is the difference between 12 successive perfect fifths, (3/2)12 : 27 (= 129.746338) and 7 octaves, 27 (= 128).

The greater diesis is the difference between four successive just minor thirds  (6/5)4 (=1,296 : 625 = 2.0736) and the octave, 2:1.

... Or is it really the other way round: Numbers incarnating through music?

This content has been seen 2428 times

Comment

Join Overtone Music Network

## Latest Activity

Bernhard Mikuskovics posted an event

### OBERTONGESANG (Workshop, Wien) at Zentrum für geistige Heilweisen

March 21, 2018 from 10am to 4pm
Eintagesworkshop für AnfängerKursinhalt: Grundlagen des Obertongesanges in Theorie &…See More
Mar 18
Aionigma posted a blog post

### AIONIGMA Oberton.Sommer.Retreat Kärnten 2018

Liebe Freunde der Obertöne! Auch heuer gibt es wieder die Möglichkeit, im Rahmen eines einwöchigen…See More
Mar 17
Aionigma updated their profile
Mar 17

### AIONIGMA: RITUS (Fujara, Overtone Singing, Didgeridoo)

"Much appreciated, Ayla! You ´re welcome!"
Mar 15
Aionigma updated an event

### Aionigma.Sommer.Oberton.Retreat (Kärnten, Österreich) at Pfarrhof Maria Wörth

July 1, 2018 at 12am to July 8, 2018 at 12am
Obertonsingen & -musizieren, Lernen, Üben, Proben, Auftreten & Relaxen an einem der…See More
Mar 14
James Robert Hester replied to the discussion 'African Thumb Piano Tuning'
"Hi Andy, The argument between African and European origins of slave songs has been going on now…"
Mar 2

### Zwischenwelten KFB Trailer

"Sehr interessant und vielseitig. Hat mich in den bann gezogen. Ich könnte mir sehr gut dazu…"
Mar 2
tomasz marcin fudala updated their profile
Feb 28