Mad Science Tuning


Below is a version of the Berlioz symphony (in 7-limit minimax Pajara[12]); this famous piece amazingly dates from 1830. This version of it is not for the faint of heart nor musical purists, but it would be excellent, along with the porcupinized Bald Mountain, for Halloween.

Symphony Fantastique Mv 1 10.02 mb

Movement 2 6.51 mb

Movement 3 15.79 mb

Movement 4 4.37 mb

Movement 5 6.90 mb


Wreckpop is the meantone scale

C C# D Eb E F F# G Ab A A# Cb

where the tuning should to meantone with fifths as flat as 31-et or a bit flatter--the neighborhood of 50-et is best. It can be used, by those not adverse to xenharmonies, as an alternative to Meantone[12]. The tuning used below is 50-equal.

Debussy String Quartet Mv 1 6.33 mb

Ravel String Quartet Mv 1 8.05 mb

Ravel Movement 2 4.62 mb

Ravel Movement 3 9.02 mb

Ravel Movement 4 7.1 mb


Moussorgky's Night on Bald Mountain isn't precisely found below; it has been "porcupinized" to the scale, given in terms of generator steps of Porcupine, -6, -4, -3, -2, -1, 0, 1, 2, 3, 4, 6. The tuning used has the generator as 3/22 octave, so it is 22-equal tuning. The second piece is a porcupinized version of Joe Monzo's version of the first movement of Mahler's seventh symphony. It ends up being in Porcupine[16].

Night on Bald Mountain 12.15 mb

Mahler's Pet Porcupine 27.34 mb

Commatic scale

We can, if we like, mix intervals such as 64/63 and 81/80 among much larger scale steps.Following up on some suggestions of Robert Walker, I concocted the following scale: 10/9, 9/8, 5/4, 21/16, 4/3, 3/2, 27/16, 5/3, 7/4, 16/9, 2. Note I have put 27/16 before 5/3 in the ordering; this was done so that retunings using this scale would have more pure triads when the patter of steps 0-4-7 or 0-3-7 is used. Using this ordering, we have from 0-4-7 a 1-6/5-3/2 on degrees 1 and 8, a 1-4/3-14/9 on degree 2 and a 1-4/3-8/5 on degree 11. 0-3-7 nets us 1-5/4-3/2 on degrees 5 and 10, a 1-6/5-8/5 on degree 11, a 1-9/8-3/2 on degree 8, a 1-8/7-3/2 on degree 9, a 1-9/7-10/7 on degree 4, a 1-189/160-3/2, which in effect is a 1-13/11-3/2, on degree 1 and various other chords. Below is the first movement of Prokoviev's first piano concerto in this scale; the scale is employed so that the tonic, Db, is the 10/9.

Prokoviev First Piano Concerto 17.8 mb


It is possible to warp a piece in meantone, with comma 81/80, to and from one in pelogic, with comma 135/128. (It's also possible to warp either to slendric, with comma 1029/1024, which I think is more interesting; see Saxfare in 36 Equal.) Below Couperin's Les Barricades Mysterieuses has been warped to pelogic. Mysterious Mush is the result with partials tuned to TOP pelogic; Mysterious Just has them in integer relationships.

Mysterious Mush 2.61 mb

Mysterious Just 2.66 mb

A related idea is to tune to a JI scale with 135/128 as a comma. Three twelve-note Fokker blocks can be constructed from 125/108 and 135/128, which give a scale which can be ordered according to the resulting val, which is <12 19 27|. Below I have tuned the radiant Dona Nobis Pacem from Bach's Mass in b minor to one of these scales: 1 10/9 9/8 5/4 6/5 4/3 25/16 3/2 5/3 8/5 15/8 25/12. It comes out sounding very different!

Dona Nobis Pacem 3.44 mb

Below is a justly-famous aria for the Queen of the Night in the justly-famous opera The Magic Flute by the justly-famous Mozart. It is sung by the justly-infamous Florence Foster Jenkins in a clearly xenharmonic manner. However, no one knows nor ever can know what scale she used.

Der Hölle Rache 114 kb