More than a year before I wrote this piece, my then eleven-year-old son Bernard began to insist repeatedly that I write a piece called How Miraculous Things Happen. I don't know where he got the idea. I began my fourth Tuning Study without a title, and finally realized that Bernard's title had an intriguing relationship to what I was writing; enough so to try out the title and see where it led the piece. I was dealing, after all, with the transformation of disappointment into triumph, or - on a more literal level - the gradual transformation of minor into major, along a series of microtonal steps. The piece is dedicated, naturally, to Bernard.

The scale employed contains 24 pitches per octave in an eleven-limit just-intonation system, two of those pitches appearing only in the final measures. Although there are 24 pitches, this is not at all a quarter-tone scale; some pitches are crammed close together, others approximate the regular chromatic scale. The scale (given in Ben Johnston's notation) is as follows:

Pitch:	A	A^-	A#	B-	B	BL-	C7	C	C^-	C#	C#L	D7
Ratio:	1/1	55/54	25/24	10/9	9/8	8/7	7/6	6/5	11/9	5/4	9/7	21/16
Cents:	0	32	71	182	204	231	267	316	347	386	435	471

D-	D#L	E-	E	F7	E#	F#	F#L	G-	G#	G#L	A7
4/3	10/7	40/27	3/2	14/9	25/16	5/3	12/7	16/9	15/8	40/21	35/18
498	617	680	702	765	773	884	933	996	1088	1116	1151

(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, L raises 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.

The basic idea of the tuning was similar to that of Superparticular Woman, the most important line being a series of superparticular ratios leading from B (10/9) to C# (5/4). (A superparticular ratio is one in the form (x+1)/x, such as 5/4 and 6/5.) One of the effects I seek in my just intonation music is to render audible the different roles of pitches that are very close together within a given key, and How Miraculous Things Happen succeeds perhaps better than anything I'd written earlier. The tuning results from the pitches from B- up to C#, and from D- down to C#, accompanied by the chords most relevant to the key of A needed to support them and make their harmonic function clear (the root of each chord is given in boldface):

Cents:	182	204	231	267	316	347	386	435	471	498
Melody:	B-	B	BL-	C7	C	C^-	C#	C#L	D7	D-
Hamonies:	G-	G#	A	A	A	B-	A	BL-	B	A
	D-	E	F#L	F7	E	G-	F#	F#L	G#	F#
		D7	D#L	D-		D-			E

The primary background melody, then, employs ten pitches within a minor third, from B- to D-. The C (C7) that is the seventh of the subdominant chord is different from the C that is the third of the tonic minor, and the B that is the fifth of the dominant chord is different from the B (BL-) that is the tonic of the chord in which A is the seventh; these differences, purely theoretical in most contexts, here become quite audible. The effect, I find, is that the pitches are so well supported by pure harmonies that people often fail to be disturbed by the slight pitch shifts. Some musicians don't even register that I'm using many more than 12 pitches to the octave, because the harmonies sound so pure, simple, and familiar. I enjoy that response. I use microtones not to make the music sound weird or unfamiliar, as so many microtonalists do, but to make the music more beautiful.

How Miraculous Things Happen opens in A minor and keeps trying to move from B through C up to C# to become A major; but every time it reaches C#, the bass shifts to create F# minor. At the end of the work, A moves up through A^- to A#, for a close in F# major. The piece succeeds in moving to a major key, but not the key it was originally aiming for. That's how, it seemed to me, miraculous things happen.

The piece was slightly revised in March 2008.

Secelcted performances (by the composer unless otherwise noted):
May 23, 1997 at the American Festival of Microtonal Music, NYU Frederick Lowe Theatre (world premiere)
February 24, 1999 at Olin Auditorium, Bard College
February 13, 1999 at the Ussachevsky Memorial Festival, Pomona College, by Genevieve Lee
November 12, 1999, at Kulas Recital Hall, Oberlin College
April 15, 2000, at Cornish College of the Arts, Seattle

Kyle Gann

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