Microtonal, just intonation, electronic music software Microtonal, just intonation, electronic music software

Encyclopedia of Microtonal Music Theory

@ 00 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Login   |  Encyclopedia Index

Analysis and Tonescape video of Ben Johnston: Quartet 9

[Joseph Monzo]

© 2013 by Joseph Monzo

Johnston, Quartet 9, 2nd movement, perfomed in Tonescape

Ben Johnston (1926-2019) was one of America's most important pioneering microtonal composers, specifically focusing on what he called "extended just-intonation." On this page I present an analysis of the 2nd movement of Johnston's 9th Quartet, accompanied by a Tonescape video of the piece.

The 2nd movement is in a classical scherzo-trio-scherzo (ABA) form. Each of the main parts (A and B) is divided into two sections of 14 measures each. Each section is repeated when appearing for the first time, then Johnston directs the players to perform the A section again without repeats to conclude the movement.

The tuning of the 2nd movement is 17-limit extended just-intonation for the scherzo (A) section and 15-odd limit / 13-prime-limit JI for the trio (B) section. The scherzo (A) section uses exclusively otonal ("major") harmonies, and the trio (B) section uses exclusively utonal ("minor") harmonies.

movement 2, part 1, section 1

measures   tonality  odentities
[1-14     : 1/1-o    1-3-5-7-9-11-13-15-17
[i.e., entire section]

movement 2, part 1, section 2

measures   tonality  odentities
[1-2]     : 3/2-o    1-3-5-7-9-11-13
[3-4]     : 6/5-o    1-3-5-7-9-11-13-15
[5-6-7]   : 27/25-o  1-3-5-7-9-11-13-15-17
[8-9]     : 36/25-o  1-3-5-7-9-11-13
[10-11]   : 9/5-o    1-3-5-7-9-11
[12-13-14]: 1/1-o    1-3-5-7-9-11-13-15

movement 2, part 2, section 1

measures   tonality  udentities
[1-14     : 5/4-u    1-3-5-7-9-11-13-15
[i.e., entire section]

movement 2, part 2, section 2

measures   tonality  udentities
[1-2]     : 5/3-u    1-3-5-7-9-11-13-15
[3-4-5]   : 4/3-u    1-3-5-7-9-11-13-15
[6-7-8]   : 10/9-u   1-3-5-7-9-11-13-15
[9]       : 25/18-u  1-3-5-7-9-11-13-15
[10-11]   : 5-3-u    1-3-5-7-9-11-13-15
[12-13-14]: 5/4-u    1-3-5-9

I can confirm that Johnston himself made mistakes in hand-writing his scores which were precisely a result of his system of notation -- specifically, using the 2-dimensional 5-limit C-major scale as the basis for his nominals ABCDEFG and the sharps/flats (and double-, triple-, etc.), instead of using the 1-dimensional 3-limit pythagorean tuning as his basis (as is done with HEWM, HEJI, and sagittal notations). By making versions of his pieces in Tonescape, the lattice makes it obvious when there is a particular note in his score which appears in the wrong place in the lattice, and it is always a result of Johnston omitting or incorrectly including a + or - in the accidental. Unfortunately I did not include here my list of errata; I wish I had, because as of 2023 I don't have access to my papers - hopefully someday I will find them and add my research notes here.

. . . . . . . . .

Please make a donation to help keep Tonalsoft online.

Thank you!