An avant garde piece for a piano retuned to just intonation. May be of interest to pipers and other fans of beatless intervals.
Thanks for the link! I’ve been a pianist for over 25 years and had forgotten about just intonation. Not something you run into every day, but I must say it is rather inspiring to hear something so “different”.
I wonder if I can take a dremel to my pipe chanter and become the first minimalist piper? 
Matt
your pipe chanter should, of course, already be tuned for just intonation… as should any drone-based instrument (for instance those in the Indian Classical traditions).
Thanks for that Kevin it is a wonderful piece for meditation purposes..brilliant…go raibh mile maith agat.
Glad you liked it, Uilliam. There’s a lot of chill-out avant garde music, much of Young’s output, Terry Riley, Phillip Glass, Eno, John Hassell. “Furniture Music” Eno originally dubbed it, but it became marketed as “Ambient.”
Indeed there’s even a Just Intonation Network. Modern pop music sounds like it has been digitally retuned to pure intervals; you certainly don’t hear hideously out-of-tune moments like the guitar solo in Wipe Out anymore. Any thoughts there, Bill?
A piano cannot be tuned Just because it’s a fixed pitch instrument, unlike others that can adjust as they go like voice and violin–except for its open strings, etc. Parts of a piano can be tuned just, that is, certain limited intervals. The tune played on U2b is basically an A minor chord with a D bass and it’s octave. The only notes played are D,A,C,and E. It may be possible to tune one triad pure on the piano, if I remember right, but now that I think about it there may be a problem getting the 5ths and 3rds in the triad both pure. I think it’s one or the other. I tried it once to find out, but it’s been a few years. The wolves started howling almost immediately.
With your chanter each note is tuned as pure as possible to the drone (bag pressure held steady) but if you could hear the different notes of the chanter’s scale played against each other the intervals would probably not be pure. Purity often becomes more of a perception than a reality. Whistles are notorious for their overwhelming beats while playing harmony.
A piano can be tuned so as to play limited pieces in Just Intonation - however it severely restricts the keys, modes, and harmonies possible. Lorenzo is right insofar as a fixed pitch instrument cannot play in pure “JI” over any kind of “normal” range.
However Irish traditional music is not harmonic music, it is melodic (or drone-based melodic, if there is a precise musicological term for this). Thus the issue of “internal” thirds, fifths, etc. in the scale doesn’t normally arise (except when playing regulators). I suppose the old harp tradition may have been an exception, insofar as there was some limited harmony tradition there - probably the harpers were in effect using some complex asymmetrical temperament that favored certain keys. They certainly weren’t using equal temperament!
With pianos there is another serious issue - inharmonicity; since piano notes are by their nature percussive, the harmonics of individual notes are not in fact in perfect integer relationship, whereas they are guaranteed to be so for sustained tones on a wind instrument.
Kevin, I’m sure all modern music is ET - especially pop music. Our ears have just become deaf to the monstrous ET third. Play a proper JI third nowadays and folks are likely to think it’s too narrow (however Benade showed that even experienced musicians were shocked by the dissonance of the ET third when presented it out of context, alongside a JI third).
Bill
“shocked by the dissonance of the ET third”
perhaps this is why most car horns play a major third. Not pleasant at all.
Though I have no idea if it’s ET or not.
one solution from the world of appliances.
Thanks for that link. Really great to hear those intervals on the piano. I don’t know about being the first minimalist piper but I did just play “In C” with Terry Riley, Kronos Quartet, Phillip Glass and about 60 other folks at Carnegie Hall a couple of weeks ago. What a great time with a great K&Q C chanter.
He sounds as tho he is introducing a Batman movie 
Is his voice in ET or JI??
Not meaning to belabor the point, I did find my previous experiment and would like to share it with those who may care. Here’s the details why a piano (meaning the whole piano) cannot be tuned Just. In the following I only tried tuning the white keys. The terms “pure” and “Just” are used interchangably.
(tuning octave C3 through C4 - meaning the middle range of the piano)
Starting with the low C…
- interval C-E was tuned pure (3rd)
- interval C-F was tuned pure (4th)
- interval C-G was tuned pure (5th)
- interval C-A was tuned pure (6th) A can be double checked against F. Both the 6th and 3rd should be a mirror of each other
- interval C-D was tuned pure (2nd) (obtained by tuning D pure against the G)
- interval C-B was tuned pure (M7th) (obtained by tuning B pure against the E)
- the octave is always tuned pure
When the D note was sounded against the A note, all hell broke loose. The dissonance was unbearable.
When the G chord was played (D-G-B) the interval D-B (a 6th) wavered badly. B was tuned from the E (a 5th).
The F chord (C-F-A) sounded good, Am chord sounded good (C-E-A), Em chord (E-G-B) sounded kind of weird (G-B wavered), the G chord (D-G-B) was harsh, as was the Dm chord (D-F-A).
The worst interval created, by tuning these seven white keys pure to the root, was the D-A interval. Unbearable. D was tuned pure from the G. I tried tuning D pure from the A, but the D-G interval headed south just as bad. The reason for tuning the D to the A or G is because I wouldn’t know how to tune a D note to C (a 2nd) by using only the ear.
Three chords sounded good: C, Am, and F. Three (or four) chords sounded bad: G, G7, Em, and Dm.
The chromatic scale on fixed instruments means one thing: there has to be a compromise (imperfection) between every interval in order for the whole thing to sound tolerable, and to fit within the octave, otherwise the last note would end up about 42 cents sharp. This is just a strange phenomena found in nature we must live with. We couldn’t live with the octave being out of tune at the expense of the other notes inbetween being pure to the root and so many intervals being unbearable.
This would in effect be a modulation upwards from the tonic one step, to a D chord. Modulated chords don’t generally work in JI as your experiment makes evident, and thus the motivation for tempering. However I disagree that the nature of fixed pitch precludes the usability of just intonation - it can still be used to good effect within its limited harmonic range.
Perhaps if we transpose upwards so that the tonic is D, this will be more intuitive in the piping context. You’d then have perfect D and G chords and crappy E major, Amajor, and E minor chords… meaning when playing an E on the chanter against a B on the regs, you could expect trouble. The other problem combo you mentioned, E against C#, can’t be played on a standard full set at all. This is all still assuming fixed pitch, which of course we aren’t quite limited to on the pipes, but it points out that in a piping context fixed pitch isn’t a big stumbling block for our limited harmonies. Many of the internal intervals would be perfect, for instance A-C#, F#-B, E-G, E-A, Fnat-A, G-B, G-Cnat, F#-B, and more that I’ve overlooked… i.e. most of the intervals actually encountered on the pipes would be “ideal” However this result does suggest that the current regulator arrangement is about the limit of what can be accommodated with theoretically “perfect” tuning; once you add notes such as E and C#, things start to break down. The same would be true of any fixed pitch instrument; for any particular starting point for Just Intonation there would be a range of “good” harmonies available. In some musical traditions it would be considered commonplace to retune certain strings on an instrument when switching modalities in the repertoire - not practical for pianos, so you could say that piano pitch is a bit “more fixed” than, say, fretted instruments or a diatonic harp.
By my calculations your G-B should not have wavered (as you mentioned in the Em chord), it should have been perfect (15:8/3:2 or 5:4), perhaps you meant the E-B interval again (corresponding to F#-C# in our transposed version). (Mmmm, F# minor, Whinny Hills of Leitrim anyone?)
For anyone who might not have caught it, the name “well tuned piano” is of course a reference to J.S. Bach’s “The Well-Tempered Clavier”. Many folks in the past took this as a milestone in ET but in fact it has recently been proven convincingly (2005) that Bach’s “well tempering” was in fact a “circulating temperament” which is asymmetrical but contains quite a few just intervals. In Bach’s tuning, while all keys are usable, some sound better than others, which is something which I am told is used to advantage in the “W-T C” work… which was not intended to be played in ET!
That’s more of what I had in mind in re: pop music, we’ve been hearing these too perfect harmonies in music since Eventide came out with the Ultra-Harmonizer in the early 90s. Interesting that they’re still working on purity-on-the-fly for recording engineers’ Brave New World where dissonance has been banished forever. Let’s grab a pint of soma!