Encyclopaedia of Tuning

© 2004 Tonalsoft Inc.

19-tone Samba

© 1998 by Joe Monzo

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':

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'.

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


(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.

. . . . . . . . . . . . . . . . . . . . . .

Some theoretical musings on the harmonies in 19-tone Samba

Main tune, 2nd chord -- D:C:E:A

    This chord functions as a dominant-7th type of harmony with D as the root, which will lead to a resolution on the following G chord. However, because the "3rd of the chord" is not present, it may be construed as either a regular dominant-9th or as an 11th.

    interval analysis:

    • D:C is functioning as the "minor-7th" interval, and approximates 9:5 ratio, and more closely 52:29.

    • D:E is a "major-9th", approximating 9:4, and more closely 29:13.

    • D:A is a "major-12th" ("perfect-5th" + "8ve"), approximating 3:1, and more closely 239:80.


      2002.09.28 -- reformatted font of diagrams
      2004.07.12 -- started "theoretical musings" section

    2002.09.28 -- reformatted font of diagrams
    2004.07.12 -- started "theoretical musings" section