Kyle Gann: Cinderella's Bad Magic

Cinderella's Bad Magic is an opera in one act for five voices, flute, three synthesizers, and fretless bass, based on a libretto by Jeffrey Sichel. The libretto is experimental, and non-narrative. There is no plot as such, but there is a spiritual journey taken amid archetypal figures of one's life. The theme of the opera is waking up: waking up from a dream, from one's neuroses, from the inauthentic sense of oneself inherited from childhood. The opening words are "Wake up!" The main character is that famous sleeper Rip Van Winkle, who sings, "One day I went to sleep and woke up and found that I had wasted my life and didn't have much time left." Rip Van Winkle describes Cinderella: "Cinderella, scared of herself and scared of taking a chance at being herself." And at last, he sings "The world in front of me, Cinderella behind me." Rip Van Winkle and Cinderella navigate their way between a cruel, dogmatic father with overtones of Stanley Kowalski in A Streetcar Named Desire and a murderous mother reminiscent of Medea. There are many other cultural references underlying the text, but the resonances tend to be global, not following consecutive lines, but echoing back and forth among different parts of the work. It is a dark and mystifying but touching, transformative work.

Read the libretto here. Read the program notes here.

The entire opera is in just intonation, using 30 pitches per octave in all. Because I was writing for singers in just intonation for the first time, I limited myself to basically five-limit intervals for the voices and main structure, so that the singers wouldn't have to negotiate any intervals outside the ones they're used to from European music. This was the longest stretch of continuous music I had ever tried to write within one alternate tuning, and I needed to plan out my pitch resources carefully. To economize on pitches I set up a large scale tonal structure based on pivot tones, to maximize the number of pitches retained from key to key. The piece proceeds back and forth along the following chain of ten keys:

Eb major

C minor

C major

A minor

A major

C# minor

C# major

A# minor

A# major

Cx minor

Reading vertical three-note triads, the structural voice-leading is as follows:

								Cx	Cx
				C#	C#	C#	C#
	C	C	C
Bb
							A#	A#
			A	A
									Gx
					G#	G#
G	G	G
						E#	E#	E#	E#
		E	E	E	E
Eb	Eb

When I set E-flat as 1/1, the numbers became very complex as the tonality drifted to A# - up to 4375/3456 and 3125/2304. So I decided to take the central tonalty of A as 1/1, which meant that I started on an E-flat of 36/25. Taking all the major thirds as 5/4, all the minor thirds as 6/5, and all the perfect fifths as 3/2, this gave me a structural skeleton of 12 pitches:

Bb 27/25	C 6/5	C 6/5	C 6/5	C# 5/4	C# 5/4	C# 5/4	C# 5/4	Cx 125/96	Cx 125/96
G 9/5	G 9/5	G 9/5	A 1/1	A 1/1	G# 15/8	G# 15/8	A# 25/24	A# 25/24	Gx 125/64
Eb 36/25	Eb 36/25	E 3/2	E 3/2	E 3/2	E 3/2	E# 25/16	E# 25/16	E# 25/16	E# 25/16

I composed freely around this set of tonalities, adding in scale steps including a few seven-limit and one eleven-limit pitches, eventually arriving at a scale of 30 pitches:

Pitch:	Ratio:	Cents:	Keys:
			Eb	C	A	C#	A#
Eb	36/25	631.3	1/1	6/5
E^b-	22/15	663.0		11/9
E	3/2	702.0		5/4	3/2	6/5
E^-	55/36	733.7				11/9
E#	25/16	772.6				5/4	3/2
F	8/5	813.7	10/9	4/3	8/5
F+	81/50	835.2	9/8
F#	5/3	884.4			5/3	4/3	8/5
Fx	125/72	955.0				25/18	5/3
G7	7/4	968.8			7/4
G	9/5	1017.6	5/4	3/2	9/5	36/25
G7#	175/96	1039.5					7/4
G#	15/8	1088.3				3/2	9/5
Ab	48/25	1129.3	4/3	8/5
Gx	125/64	1158.9					15/8
A	1/1	0.0		5/3	1/1	8/5
A#	25/24	70.7				5/3	1/1
B7b	21/20	84.5		7/4
A#+	135/128	92.2				27/16
Bb	27/25	133.2	3/2	9/5	27/25
B	9/8	203.9		15/8	9/8	9/5
B#	75/64	274.6				15/8	9/8
C	6/5	315.6	5/3	1/1	6/5
C#	5/4	386.3			5/4	1/1	6/5
Db	32/25	427.4		16/15
Cx	125/96	457.0					5/4
D-	4/3	498.0			4/3
D	27/20	519.6	15/8	9/8
D#-	25/18	568.7					4/3
D#	45/32	590.2			45/32	9/8

The final tonality, C double-sharp minor, appears only at the very end with no further supporting pitches.

(If you don't have enough experience with just intonation to make sense of this chart, try reading the step-by-step Just Intonation Explained section.) In Johnston's notation, + raises a pitch by 81/80, - lowers it by 80/81, # raises it by 25/24, 7 lowers it by 35/36, ^ raises it by 33/32, and F-A-C, C-E-G, and G-B-D are all perfectly tuned 4:5:6 major triads.

As a five-limit structure based on triads and pivot tones, this is an easily understandable, even conventional-seeming structure. But by staying within just intonation it runs into some peculiar anomalies possibly never heard before in music - at least, not capitalized on in a structural way. By the time we get from Eb to C#, those two pitches have a relationship of 144/125, or 245 cents, virtually a quarter-tone relationship. Likewise, the relation of Eb to A# is 625/432, or 639 cents. By going back and forth between these keys, I can reveal the very distant relationships between tonalities generated through well-worn tonal modulation techniques - and still keep the opera eminently singable.

Kyle Gann

Return to Just Intonation Explained

Return to List of Compositions

return to the home page