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FJS Examples

You have seen many short FJS examples in the crash course and the formal description, as well as some longer ones in the comparison. If you haven’t seen them yet, make sure to check those out first. This page contains even more longer examples of the FJS in usage.


This is a rendition of Johann Sebastian Bach’s Prelude in C Major, BWV 846, from The Well-Tempered Clavier Book I. It uses the following tuning conventions:

An FJS key signature is also exemplified.

Listen to it:

Here you’ll find a chorale which simultaneously compares the FJS against Helmholtz-Ellis and Ben Johnston. Listen to it below:

Surely you’ve seen the introductory video for the FJS, which I’ve placed on the main page. Here, you can see a score of the music used in it, written of course in the FJS, also with a comparison.

(*) Note about the score: It’s not possible to write the 101st harmonic in either Helmholtz-Ellis or Johnston. Instead, the score reads 128/81 (Helmholtz-Ellis) or 8/5 (Johnston) at that position.


All the three above examples can also be found in video form:


This interpretation of Steve Reich’s Electric Counterpoint in 5-limit Just Intonation uses the 5-limit Tonnetz written in the FJS to visualize the tuning.

This piano cover of the Minecraft soundtrack in 7-limit Just Intonation also visualizes its tuning lattices in the FJS.

Note and Interval Naming

Harry Partch’s 43-tone Genesis Scale

P1 P15 P111 m275 m25 M211 m2115 M25 M2 M27 m37
m3 m35 m311 M35 P4711 M37 P47 P4 P45 P411 d575
A457 P511 P55 P5 P57 m67 P5117 m65 M611 M65 M6
M67 m77 m7 m75 M7511 m711 M75 M757 P811 P85 P8

Dante Rosati’s 21-tone Scale

P1 m25 M25 M2 M27 m37 m35 M35 M37 P4 d575
A457 P5 m67 m65 M65 M67 m77 m7 m75 M75 P8

Michael Harrison’s Revelation Tuning

E♭7 B♭7 F7 C7 G7      
F C G D A E B +3:2

Terry Riley’s Harp of New Albion Tuning

  A♯25 E♯25 B♯25    
B5 F♯5 C♯5 G♯5 D♯5  
G D A E   +3:2

La Monte Young’s Well-Tuned Piano Tuning

B♭7 F7 C7 G7    
C G D A E  
D7 A7 E7     +3:2

Harry Partch’s 11-limit Tonality Diamond

P1 m37 P4711 d575 m67 m77
M67 P1 M211 m35 P4 P5
P5117 m711 P1 m2115 m311 P411
A457 M65 M7511 P1 M25 M35
M37 P5 M611 m75 P1 M2
M27 P4 P511 m65 m7 P1

JI Extensions of the Major Scale

Pythagorean Major Scale (7 notes)

C, D, E, F, G, A, B, C

Ptolemy’s Intense Diatonic (7 notes)

C, D, E5, F, G, A5, B5, C

Ptolemy’s Intense Diatonic, with usable ii chord (8 notes)

C, D5, D, E5, F, G, A5, B5, C

Complete JI Major Scale (12 notes)

C, D5, D, E5, E, F7, F, G, A5, A, B5, C7, C

The Harmonic Series 1-64

C C G C E5 G B♭7 C
D E5 F11 G A♭13 B♭7 B5 C
D♭17 D E♭19 E5 F7 F11 F♯23 G
G♯25 A♭13 A B♭7 B♭29 B5 B31 C
C11 D♭17 D35 D D37 E♭19 E♭13 E5
E41 F7 F43 F11 F♯5 F♯23 G47 G
A♭49 G♯25 A♭17 A♭13 A53 A A55 B♭7
B♭19 B♭29 B59 B5 B61 B31 C7 C

Scale Listing

I have used the FJS to list the pitches I have used in a Just Intonation piece. For example, here are the tuning sets for two pieces, Overture of Opulence and Meditations on a Medieval Theme Remix, from Justin Tonation.

Using the FJS in these contexts helps me immediately recognize the function of a note even if its ratio to the initial tonic is very complex (and I do use complex ratios). For instance, 243/200 may not tell me much, but seeing that it is a m325 helps me recognize it instantly; it’s just a 6/5 raised by another syntonic comma. To give another example from another one of my pieces, Symphony of the Elements: 729/640 is confusing, but M25 is less so; a 9/8 raised by a syntonic comma.