Yep. Just looking for a chart showing the uilleann scale and how it differs against equal temperment. In particular, I’d like to find the difference in +/- cents for each note of the scale. I assume the octaves would be the same (or at least should be…let’s assume perfect reed/chanter conditions here).
I’ve been asked to explain the differences for a workshop I’m giving in a couple of months and would like to have a chart to base things on.
Back D - 0.00
C sharp - minus 11.73
C Nat - minus 3.91
B - minus 15.64
A - plus 1.96
G - minus 1.96
F sharp - minus 13.69
E - plus 3.91
Bottom D - 0.00
Because of the reference tone (the drone) the chanter is tuned to a concept known as Just Intonation. This is based on the harmonic series and intervals follow mathematical ratios e.g. semitone16/15, major tone 9/8, Perfect fourth 4/3, perfect fifth 3/2. The major scale is made up of Major tones, minor tones and semitones. Great if you are only ever going to play in just one key signature.
Problem comes when you want to play in a key other than the home key of the chanter as with this form of tuning the some notes whilst being called the same will have a different frequency depending upon the key signature. These have to be evened out (tempered) so the differences are not so noticible
There is a short section on my website on tuning but your best option would be “Fundamentals of Musical Acoustics” by Arthur H Benade and published by Dover ISBN 0-486-26484-X - a little bit OTT for what you are looking for.
So even the pipes with their “perfect” just intonation can be (and I assume very often are) detuned ever so slightly to allow for multiple keys to be performed on the chanter? This smacks of equal temperment! Though I think I see what it is you’re saying. Is there any sort of standard “de-tuning” from a true Just tuning that is accepted by pipe makers to allow this cross-key ability?
Amazing topic to me. Thanks again for all the knowledge here.
I’d guess not… that what gives the pipes their characteristic sound when played with other instruments.
Of course, there is also tremendous leeway in how much the pitch can be adjusted on the fly by the player with alternate fingerings, on/off leg notes, minor adjustments in pressure etc.
Brian, I would refer you to the Howard fingering chart which was the subject of some controversy and quite a lot of character assaination some time back. Whatever anyone may think about the appearence of his pipes, (and I quite like them) they do play in tune in both octaves, and his fingering chart shows how many cents sharp or flat they need to be.