GAELIC HARP TEMPERAMENT
The tuning systems presented by Bunting and Bell indicate a Pythagorean tuning system. The
next few pages describe the physical measurements of the tuning, ie, the musical intervals.
The reader will need to be familiar with the steps of the 12 note scale of Western Europe.
Intervallic measurements will be presented here mainly using the cents system of Alexander
John Ellis (1814-1890) which is the best rule for comparing the sizes of different intervals.
When intervals are referred to as fifths, fourths, etc, the measurements will be those of
Pythagorean temperament and not in accordance with equal temperament.
Whole tone (major 2nd): the meízon tone
The octave equals 1200 cents, a fifth equals 701.96 cents, and 4th equals 498.045 cents
(representing the ratios of 2:1, 3:2 & 4:3 respectively).
The difference between the 5th (701.96 cents) and 4th (498.045 cents) is a whole tone (major
2nd) measuring 203.91 cents (9:8). The Greeks call this "ο μείζων τόνος" (the greater tone)
which is why it is called the major (lit. greater) 2nd. So, in rough numbers, 702 - 498 = 204.
How the meízones are formed can be shown in relation to the first octave tuned on the Gaelic
harp, ie, G a b c d e f g.
8ve
5th
5th
8ve
By tuning G-d, d-aa and aa-a, the interval of G-a has been tuned. The 4th and 5th are known
4th & 5th
and a subtraction can be done of 702 minus 498,
5th
4th
working out the value of the meízon, the basic whole tone of Pythagorean tuning.
2nd
Tuning by 5ths in this way produces 3 basic whole tones (2nds), all of 204 cents.
5th G - d aa-e
5th d - aa e-bb
2nd g-aa / G-a aa-bb / a-b
5th d-aa
5th aa-e
2nd d-e
This produces the scale G a b - d e - g. The intervals b-d and e-g are not whole tones but
intervals of 294.135 cents (a ratio of 19:16) and called minor (lit. lesser) 3rds.
G - 204 - a - 204 - b - 294 - d = 702
d - 204 - e - 294 - g - 204 - a = 702