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.

Notation

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:

4:5:6(:15) for major triads (seventh chords);
10:12:15(:18) for minor triads (seventh chords);
4:5:6:7 for dominant seventh chords;
10:12:14:17 for diminished seventh chords.

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.

Videos

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

Additionally:

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

+7:4
E♭⁷	B♭⁷	F⁷	C⁷	G⁷
F	C	G	D	A	E	B	+3:2

Terry Riley’s Harp of New Albion Tuning

+5:4
	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

+7:4
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.