An Organ for Music in «Extended Tonality»*
Tuning: Concert pitch c = 128 Hz, a′ = 429 Hz.
Unequal temperament (Johann Sonnleitner)
Three fifths (c – g, g – d, d – a) 1/6 comma narrow,
Six fifths (a – e, e – h, h – f-sharp and e-flat – b-flat, b-flat – f, f – c)
1/12 comma narrow,
Three pure fifths (f-sharp – c-sharp, d-flat – a-flat, a-flat – e-flat).
From each of the 12 notes one tunes an «Alphorn-Fa» 11/8, giving a
nearly perfect 24-note cycle of harmonic fourths.
The pipes are arranged in third-seventh divisions to benefit the natural
sevenths 7/4 that are somewhat disadvantaged because of the quartertone
* In «extended tonality» the major and minor scales after slight adjustments
in accordance with the proportions of the harmonic series from
the eighth to the 14th harmonic (in the major mode) and their inversion
(for the minor mode). Slightly tempering the exact mathematic relationships
makes enharmonic transformations possible.