Written November 1998, in San Diego, on one of Ivor Darreg's 19-tone guitars.

(Download the MIDI-file or mp3.)

This piece is in 19-tET tuning, and is an example of a microtonal piece that does not sound xenharmonic at all - to my ears, anyway. (The two terms are often assumed to be synonymous.)

The notational convention follows that used by Neil Haverstick in his book 19 Tones, A New Beginning, but here referenced from 'E' instead of 'C':

19-tET
degree Semitones  Note

 (19  12.00   E )
  18  11.37   Eb
  17  10.74   D#
  16  10.11   D
  15   9.47   Db
  14   8.84   C#
  13   8.21   C
  12   7.58   B#
  11   6.95   B
  10   6.32   Bb
   9   5.68   A#
   8   5.05   A
   7   4.42   Ab
   6   3.79   G#
   5   3.16   G
   4   2.53   Gb
   3   1.89   F#
   2   1.26   F
   1   0.63   E#
   0   0.00   E

The piece is very tonal, centered on 'D', and its tuning implies very basic Pythagorean intervals in the bass (it's really almost a drone), diatonic melodic intervals in the top voice, and diatonic and chromatic intervals in the middle voices.

Part of the reason it does not have a 'strange' sound is that it uses only a subset of the entire gamut of pitches, a 9-out-of-19 scale, which is composed of the 'D-major' scale and the two chromatic pitches 'C' and 'Bb'.

19-tET
degree Semitones  Note

  19  12.00   D
  17  10.74   C#
  16  10.11   C
  14   8.84   B
  13   8.21   Bb
  11   6.95   A
   8   5.05   G
   6   3.79   F#
   3   1.89   E
   0   0.00   D

While the "4ths" and "5ths" in this tuning are characteristic of a meantone tuning, the "3rds" and "6ths" imply those of 5-limit JI very well. These are two of the main reasons why the piece sounds so 'ordinary'.

19-tET is nearly identical with 1/3-comma meantone tuning extended to 19 tones.

This piece is very easy to play on a refretted 19-tET guitar, with the open strings tuned as in my diagram. Below is the tablature for 19-tET guitar, for each chord as it appears in the piece.

Intro:                Main tune:

    2 x 3                                          2 x
  ----------                                    ----------
 /          \                                  /          \
   D9     G      A11   Dmaj7   D9   G    Gmin   Dmaj7  A11

E---8-----5------0---|----3----8----5----5-8-5----3----0----
B---8-----5------0---|----3----8----5----5-5-5----3----0----
G---8-----6------0---|----3----8----6----5-5-5----3----0----
D---0-----0----------|----0----0----0----0-0-0----0---------
A----------------0---|---------------------------------0----
E--------------------|--------------------------------------

(Putting the fingers in the same general places - measured by distance, not by fret-number! - on a regular 12-tET guitar, will result in a performance which sounds very similar to this one. I suppose the same would be true of several other ETs.)

Here's the score of the guitar part (click on it to reload the mp3):

For more info on why 19-tET is such a good and practical approximation allowing 5-limit JI-type harmonic structures, by one of its most illustrious advocates, see my summary of Woolhouse's book.

Updated:

2002.09.28 -- reformatted font of diagrams 2001.07.10 2000.10.22

For many more diagrams and explanations of historical tunings, see my book. If you don't understand my theory or the terms I've used, start here or try some definitions.

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