Stopper Tuning

Stopper tuning based on equal division of pure twelfths (octave and fifth) or Pure Twelfth Equal Temperament (EUROPIANO 3/1988)² has become the standard on concert stages all over the world in just 30 years. 

The tempered intervals of this tuning create a strong beat masking effect, so that a very clear and resonant sound results.

The Stopper tuning is available for concert tuners and technicians with my tuning app Tunic OnlyPure, or by ear using the OnlyPure method.

I regularly give lectures and seminars for colleagues, e.g. at the PTG 2008 conference on the new OnlyPure tuning software: Stopper Temperament.

A new sequence was presented for tuning the Stopper tuning by ear with a new equal beating interval test, which considerably limits possible chain errors, at the PTG conference in Tucson, Arizona in 2019: Tuning Sequence Stopper Temperament

for the PTG convention in Kansas City 2011, the following video was made with Grigory Sokolov:

 

Stopper tuning = transformation of the Pythagorean tuning by replacing octaves 2/1 with acoustic octaves Ω=2s/1 in every interval¹

Philosophically interesting, that the Pythagorean tuning (in which any interval is formed from exponential fractions of numbers 2 and 3) is transformed into the Stopper tuning by simply replacing in the frequency ratio of the Pythagorean intervals all octaves parts of size 2/1, with acoustic octaves Ω (which are melodically perceived as "more in tune") of the size 2s = 2.0014269..., ( p = pythagorean comma = 3^12/2^19 and s= p^(1/19 )= Stopper tuning comma)*

(1): B. Stopper (1990) publication with Dodekachord(a twelfth repeating keyboard) at the Musikmesse Frankfurt

(2): B.Stopper, "Das Duodezimsystem als den natürlichen Teiltonverhältnis entsprechendes Tonsystem, Euro Piano 3/1988"

*with stringed instruments, the stiffness of the strings must also be taken into account, which also affects the octave size 

Pythagoräische Intervalle Stopper Stimmung Intervalle Harmonische Intervalle
2/1
Ω/1
2/1 (Octave)
3/1
3/1
3/1 (Twelfth)
3/2
3/Ω
3/2 (Fifth)
4/3 = 2^2/3
Ω^2/3
4/3 (Fourth)
81/64 = 3^4/2^6
3^4/Ω^6
5/4 (M3)
27/16 = 3^3/2^4
3^3/Ω^4
5/3 (M6)
9/8 = 3^2/2^3
3^2/Ω^3
(maj. sec.)
32/27 = 2^5/3^3
Ω^5/3^3
6/5 (m3)
16/9 = 2^4/3^2
Ω^4/3^2
7/4 (m7)
243/128 = 3^5/2^7
3^5/Ω^7
8/15 (M7)
256/243 = 2^8/3^5
Ω^8/3^5
(minor sec.)

(Table: partial list of pythagorean intervals) Pythagorean intervals with ambiguity become merged in the Stopper tuning. For example the diminished fifth with 2 ^ 10/3 ^ 5 and the increased fourth with 3 ^ 6/2 ^ 9 have a different value with Pythagoras, in the Stopper tuning the acoustic octave leads with Ω ^ 10/3 ^ 5 and 3 ^ 6 / Ω ^ 9 to the same result, namely the tritone of size 1.41471797...!