The Well-Tuned Piano

Western piano tuning vs. Young's tuning for The Well-Tuned Piano[10]

Piano key	12-TET (cents)	WTP (≈ cents)	Johnston's notation	Interval ratio	Frequency (≈ Hz)
E♭	000	000.00	E♭	1/1	297.989
E♮	100	176.65	F++	567/512	330.000
F	200	203.91	F+	9/8	335.238
F♯	300	239.61	G♭+	147/128	342.222
G	400	470.78	A♭+	21/16	391.111
G♯	500	443.52	A♭++	1323/1024	385.000
A	600	674.69	B♭+	189/128	440.000
B♭	700	701.96	B♭	3/2	446.984
B♮	800	737.65	C♭+	49/32	456.296
C	900	968.83	D♭	7/4	521.481
C♯	1000	941.56	D♭+	441/256	513.333
D	1100	1172.74	E♭+	63/32	586.667
E♭	1200	1200.00	E♭	2/1	595.979
Note that the 12-TET cents are all relative to Young's Eb that is 74.69 cents flat, which puts A at exactly 440 Hz.[11]

Magic chord (as played).[12] Play 

La Monte Young's piano tuning is an essential aspect of The Well-Tuned Piano. Young dates the piece as "1964–73–81–Present" to indicate the work's development through its tunings, where in E was retuned in 1973, and C♯ and G♯ were retuned in 1981.[13] Young had kept the tuning a secret until 1993, when he allowed Kyle Gann to publish the details.[14]

Young has always performed The Well-Tuned Piano on a Bösendorfer Imperial Piano, which is larger than a standard acoustic grand piano, spanning eight complete octaves, with nine notes extending the bass of the piano.[15] Young describes the pitches of his tuning as being, "derived from various partials of the overtone series of an inferred low fundamental E-flat reference ten octaves below the lowest E-flat on the Bösendorfer Imperial."[16]

As explained by Kyle Gann,[17] Young's system uses seven-limit tuning, a just intonation system where every pitch class in the scale is constructed from a previously constructed pitch by taking only up to the seventh pitch from its overtone series or undertone series. Young cites a distaste for the fifth harmonic, so Young uses only overtone and undertone numbers 2, 3, 4, 6, and 7 in the construction of his scale. A consequence to this is that the ratio between the frequencies of any two pitches is a rational number whose numerator and denominator have prime factors consisting only of 2, 3, and 7. Factors of 2 correspond to octave shifts, so in tuning theory ratios are normalized to lie within the octave 1/1–2/1 by multiplying or dividing through by powers of 2.

All of the pitches in Young's scale can be placed in a two-dimensional grid,[18] where pitches on the horizontal axis are related by a 3/2 ratio (a perfect fifth) and pitches on the vertical axis are related by a 7/4 ratio (a harmonic seventh). This collection of 12 pitches is then assigned to the keys of a standard piano keyboard in such a way that pitches with a 3/2 ratio tend to span 8 keys, which in standard piano tuning forms a perfect fifth. Each octave of the piano follows the same sequence of intervals. The following table shows the grid along with the assignment to piano keys:

The A key on the piano is tuned to A440, and the rest of the keys are tuned relative to this. This puts Young's Eb key 74.69 cents flatter than the Eb in equal temperament with the same A. It should be stressed that the key names are not meant to be tunings of the standard pitch names, and they are merely assignments of pitches to conveniently located piano keys. Some pitches, for example G♯ and G, are acoustically in reverse order.

The primary consonant intervals in Young's scale are[19]

In 12-TET, all intervals, when measured in cents, are a multiple of 100. According to Kyle Gann, when listening to The Well-Tuned Piano "you spend the first four hours becoming familiar with the cozy septimal minor third, the expansive septimal major third, and by the fifth hour you can hardly remember that intervals had ever been any other sizes."[19] In 5-limit tuning, the major third is usually a 5/4 ratio (Play ), which at 386.31 cents is closer to a 12-TET 400 cent major third than the 9/7 septimal major third (Play ) at 435.08 cents.[10] As another point for comparison, in three-limit tuning the Pythagorean major third is an 81/64 ratio, which is 407.8 cents.

A tuning is a choice of pitches in a scale, which lets one judge the intonation of pitches, and a temperament is a tuning where compromises are made to an ideal tuning (like just intonation) to meet other requirements, such as being able to use any pitch as the tonal center for Western harmonic practice. Bach's The Well-Tempered Clavier took full advantage of the development of a temperament where all 24 major and minor scales were reasonably usable. In contrast, Young's The Well-Tuned Piano is organized around certain fixed non-transposable sets of pitches that function as scales, such as the Magic Chord. While just intonation eliminates rough beating between the harmonics of two pitches, the tradeoff is the loss of general transposability to other tonal centers due to 2, 3, and 7 being coprime and pianos having a physical limit to the number of keys per octave.

The Well-Tuned Piano, being improvisatory in nature, as well as ever-changing, has no specific form. The closest a listener can come to understanding the structure of Young's piece is by studying the liner notes from the 1981 Gramavision recording. Within the liner notes, Young breaks the performance into seven major sections and further deconstructs each of those sections into multiple subsections. The sections and subsections are not notated or described, but simply listed along with the duration of each section so a listener can easily follow along.[20] The seven major sections are as follows.

1. The Opening Chord (00:00:00-00:21:47)
2. The Magic Chord (00:21:47-01:02:29)
3. The Magic Opening Chord (01:02:29-1:23:54)
4. The Magic Harmonic Rainforest Chord (1:23:54-03:05:31)
5. The Romantic Chord (03:05:31-04:01:25)
6. The Elysian Fields (04:01:25-04:59:41)
7. The Ending (04:59:41-05:01:22)

The subsections are often called themes, and each is vastly and descriptively labeled. A few examples are "The Flying Carpet", which belongs in The Romantic Chord section, and "Sunshine in The Old Country", which is found in The Magic Opening Chord section. Each theme is made up of a specific, unique combination of pitches. However the smaller themes found in one larger section will often have many pitches in common.[21]

The playing waxes and wanes, with the slow parts ritualistically simple and repetitive and the fast parts whirling and flurring notes together into eerie, independently generated voices….This sort of music is certainly not for everyone, and even for those who respond to it, there is sometimes the question of whether it should be concentrated on, meditated upon or simply lived through. Whatever one does, Mr. Young remains a fascinating if austere figure in our musical life.

— John Rockwell, The New York Times (1975), [25]

The grand performing space was dimly lighted with magenta lights. There were no chairs. Listeners wore no shoes, reclining on plush white rugs….The work lasts about four hours, and listeners are encouraged to attend numerous performances. This listener's consciousness became a little restless after two hours of overtonal influence, but Mr. Young has clearly achieved something extraordinary, creating unexplored regions of sound.

— Edward Rothstein, New York Times (1981), [26]

My personal experience with The Well-Tuned Piano was one of just such heightened concentration...the flow of momentum marshaled the vibrations of air in the room, slowly making the ear aware of sounds that weren't actually being played….I thought I heard foghorns, the roar of machinery, wood blocks, a didgeridoo, and most powerfully, the low, low vibration of the 18-cycles-per-minute E-flat that the ear supplied as the "missing fundamental" of the piano's overtones.

— Kyle Gann, The Village Voice (1987), [27]

On 3 January 2016, the 25 October 1981 Gramavision recording of The Well-Tuned Piano was broadcast on BBC Radio 3 (followed by excerpts of other Young compositions and collaborations) between 1 am and 7 am (GMT).[28]