Dreyblatt tuning system

From Xenharmonic Wiki
Jump to: navigation, search

from Arnold Dreyblatt: Tuning Systems Explanation, http://www.dreyblatt.net/general-information-music#/tuning-system/

The Dreyblatt Tuning System is calculated from the third, fifth, seventh, ninth and eleventh overtones and their multiples in the following pattern:

1 3 5 7 9 11
3 9 15 21 27 33
5 15 25 35 45 55
7 21 35 49 63 77
9 27 45 63 81 99
11 33 55 77 99 121

These mathematically related overtones are heard as tonal relationships when they are transposed and sounded above a fundamental tone. In this process of transposition from their position in the natural overtone series, these tones fall (unequally) in the span of one octave in the following order:

1, 33, 35, 9, 77, 5, 81, 21, [11,] 45, 3, 49, 99, 25, 27, 55, 7, 15, 121, 63, (2)

These tones are performed in "just intonation' based on a fundamental tone of "F".

Note Freq. Partial Cents
F 349.2 1 0
F# 360.11 33 -47
G 381.93 35 -45
G# 392.85 9 +4
G# 420.13 77 +20
A 436.5 5 -14
A 441.95 81 +8
A# 458.32 21 -29
B 480.15 11 -49
B 491.06 45 -10
C 523.8 3 +2
C 534.71 49 +38
C# 540.16 99 -45
C# 545.62 25 -28
D 589.27 27 +6
D 600.18 55 +37
D# 611.1 7 -31
E 654.75 15 -12
E 660.20 121 +2
F 687.48 63 -27