The four modes that we meet up with both in Anglo-American folk song and fiddle tunes are the Ionian (major scale), Mixolydian, Dorian, and Aeolian (natural minor scale). The first two are called "major" because the basic tonic chord is major, and the second two are "minor" for the same reason. The Phrygian mode, as well as the Lydian (and the theoretical Lochrian), are very rarely encountered. The tritone, occurs in each scale in a different place. In the Ionian mode it is seen between fa and ti (the fourth and the seventh), and in the Dorian it is between mi and la (3rd and 6th), etc. Because of the half steps around this tritone, it was considered hard to sing - diabolis in musica - and sometimes altered by raising or lowering notes in its pair. Hence, in Ionian mode F# and Bb, are common altered tones, the former going upward in melodies, and the latter coming down. Sometimes one or both notes of the tritone will be omitted from the scale altogether, which creates a hexatonic or pentatonic scale.
The term 'Celtic music' is a rather loose one; for the purpose of Ceolas, it covers the traditional music of the Celtic countries - Ireland, Scotland, Wales, Brittany (in France), Galicia (in Spain) and areas which have come under their influence, such as the U.S. and the maritime provinces of Canada, as well as some newer music based on the tradition of these countries.
The term is somewhat controversial. For starters, the Celts as an identifiable race are long gone, there are large variations in traditional music among the different countries, and many of the similarities that do exist are due to more recent influences. There is also the notion that 'Celtic' implies Celtic mysticism and a particular influence in new-age music which has little to do with traditional music. In general, the strongest connections are between the Irish and Scottish traditions and it is on these that Ceolas concentrates. Breton musicians frequently play Irish or Scottish music and at least one modern Galician group (Milladoiro) sounds quite Irish. In Canada and the U.S., the traditions are much more mixed, and it is there that the term 'Celtic' is most used, though it is also true that many groups from particular Celtic regions play the music of another region too.
It is also worth remembering that even a term such as 'Irish traditional music' is a lumping together of many different styles, from the raw, Scottish-tinged music of Donegal to the lyrical, easy-going style of Clare and many other regional styles that are only partly compatible.
Thus, in the absence of a better term ('folk' or 'world' music are sometimes used but are much vaguer), and with the realization of its shortcomings, 'celtic' is what we use for Ceolas.