The Equal Tempered Piano

If every tone of 7ET is split in half, the result is 14ET, a tuning which features Wide minor / Narrow Major 3rds and 6ths in addition to the normal complement of categorical diatonic intervals. This fugue in 3 voices uses the ambi-3rd in its chromatic subject, which is treated in inversion and augmentation. Written June 5-8, 2015.

Fugue In 14ET, a3

A scale step in 9ET is a Wide minor 2nd of 133 cents, which tends to sound wrong for any usage other than neighbor tones or in chromatic passages, so counterpoint in this tuning features a lot of arpeggiation and limited chromaticism. 9ET has the same Major 3rds as 12ET, as they are both divisible by 3. A complete circle of 9 fifths appears near the end of the piece. The meter (7/8) alternates freely between 4+3 and  3+4. Written June 12-13, 2015.

Fugue In 9ET, in 7/8

10ET has no minor 3rd, and its Narrow Major 3rd at 360 cents sounds rather out of tune unless voiced carefully, or better yet combined with a 7th. Dominant harmonies sound great in this tuning because the Small minor 7th is very nearly 4:7 (hence, the Large Major Second is also near 7:8). These smooth sounds are made use of in the fugue subject, which expands to an octave leap via a French 6th chord arpeggiation. The 10ET circle of 5ths completes in 5 steps, and all episodes are based on this cycle with occasional chromaticism and augmented 6th cadences. Written June 15-17, 2015.

Fugue in 10ET

Invention In 11ET

Adagio In 11ET

5ET is quite a limited set of pitches to work with, so this piece is very short. Written June 10, 2015.

Invention In 5ET

5ET is quite a limited set of pitches to work with, so this piece is very short. Written June 23, 2015.

Prelude In 5ET

7ET is often called "whole tone diatonic". All its steps are Small Major 2nds (smaller than the 12ET M2 by about a septimal comma). It has a Wide minor 3rd / Narrow Major 6th, and its Small 5th is smaller than meantone, but sounds similar to a meantone 5th. The 7ET circle of 5ths works well with 3rds and 7ths, and all the harmonies sound Wide minor. Written between June 13 and June 30, 2015.

The Equal Tempered Piano

Stephen Weigel