The Harp of New Albion

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The Harp of New Albion

Post  pinhedz on Sun Jun 05, 2011 10:52 am

I think LJ started the old thread on this piece--it's for piano solo in 10 parts.

LJ said that on first listening it sounds out of tune, but if you keep listening you realize that you've never heard anything so in tune.

The tuning goes back to a time before Bach. Bach promoted "equal temperment," which means that the notes of the 12-tone scale are spaced equally, so that a-sharp is the same pitch as b-flat, instead of them being two different notes.

Equal temperment is nice, because it allows you to play in all keys without retuning. That doesn't mean that you are in tune in all keys; it just means you are equally out of tune in all keys--so it's a compromise.

Bach needed equal temperment because he played in lots of different keys on the same instrument, and his music was the kind that modulates through different keys. He wrote "The Well-Tempered Clavier"--with pieces in all of the different keys--just to show how convenient it is to have your clavier tuned in equal temperment.

But, the fact remains that to be truly in tune, you can't be in equal temperment--you have to tune the old way (even though that means you have to retune every time you change key).

Why would you need to be perfectly in tune, instead of equally out of tune--Bach's way? Because if you perfectly in tune you get perfect resonance--the chords really RING. That's what terry Riley was after.

It's complicated. Terry Riley's notes try to 'splain it:


The Harp of New Albion is tuned to a five-limit chromatic scale (Figure 1) with C# as its tuning center.[5] This pitch class was a tuning constant for Riley through much of his work from the mid-80s to mid-90s. In a 1986 interview for Keyboard magazine Riley explained:

For many years I played electronic organ and synthesizers. While I was playing the synthesizers, I got together with Krishna Bhatt, who’s a sitar master living in Berkeley.[6] Krishna played in C#, so I started redoing all my pieces in C#. During that period I also started playing more and more piano. At that time I wrote the one piece that was the beginning of all the pieces I’ve done lately, called The Medicine Wheel. It was the first time I did this just tuning in C#, and I’ve kept the piano in that tuning to do both The Harp of New Albion and Salome Dances for Peace. They’re all done in the same tuning.[7]

However, none of the eleven movements of The Harp of New Albion are in the key of C#, making it necessary to distinguish here between tuning center and tonal center. For each movement Riley chooses a tonal center in varying degrees of relationship to the C# tuning center, exploiting the intervallic differences that result from choosing different tonal centers and employing different modes based on those tonal centers (Figure 2). The fact that just intonation does not transpose equally to any key was, of course, historically one of the reasons for the adoption of equal temperament. Riley's music, on the other hand, celebrates the differences in quality that result from transposition. Figure 3 diagrams Riley’s tuning system by pitch-class dyads reflecting their layout on the piano keyboard.[9] A full list of these intervals arranged by size, with their commonly accepted names in just-intonation terminology, is provided in Figure 4.

Pitch Interval Deviation
(ratio) (in cents from equal temperment)

C# 1:1 0
D 16:15 +11.7
D# 9:8 +3.9
E 6:5 +15.6
E# 5:4 +13.7
F# 4:3 -2.0
G 64:45 +9.8
G# 3:2 +2.0
A 8:5 +13.7
A# 5:3 -15.6
B 16:9 -3.9
B# 15:8 -11.7

Figure 1: Tuning in The Harp of New Albion, compared with equal temperament.[8]

... and like that.

Last edited by pinhedz on Sun Jun 05, 2011 11:16 am; edited 1 time in total

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Re: The Harp of New Albion

Post  pinhedz on Sun Jun 05, 2011 10:58 am

Here are two of the 10 parts. After a while you might start to wonder "doesn't this thing ever modulate?" (I know I do), and the answer is it can't modulate, if it did the piano would have to be retuned:

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