Western music is largely based on the major diatonic scale. This is most easily seen in the white notes on a piano keyboard, which form a diatonic scale.
If you play down a piano keyboard (i.e. from higher notes to lower notes, from right to left), just playing the white notes, where does it sound "right" to stop?
Any of the notes marked with red stars sounds satisfyingly final. These come every 7 steps along the white keys and you can see that the pattern of white and black keys also repeat their arrangement from these points.
The eight notes from one star to the next, including both stars, are called an octave. But what is special about this particular set of notes? Why does it sound different to the other sequences of eight white notes? The answer is that the white notes aren't each the same distance apart, musically. If I wanted to play a major diatonic scale on a guitar, I would press these notes:
Some notes are closer together and some are further apart; here I am not referring to the fact that the metal bars (frets) get gradually closer together from left to right, but to the fact that sometimes we jump to the next fret along and sometimes we miss one out. In fact, if we also consider the black notes on the piano keyboard, we can see that these are just the same pattern. Although the white notes appear to be evenly spaced on the keyboard, some have black notes between successive white notes and some don't. Each gap on the guitar corresponds to the presence of a black note on the piano keyboard. The pattern of steps goes gap-gap-close-gap-gap-gap-close, or 2-2-1-2-2-2-1, or, in musical terminology, tone-tone-semitone-tone-tone-tone-semitone.
When we are ringing rounds, we go from the bell with highest note down to the bell with the lowest note. So to make this sound satisfyingly final, we want our tenor to be one of the starred notes.
But, I hear you say, tenors all have different notes. This is true, but as long as we keep that pattern of steps, the bells will be in the same relationship to each other and all will sound well. We need to count up 2 steps, 2 steps, 1 step, 2 steps, 2 steps, 2 steps, 1 step for an octave. Let's try it from some random point on the piano keyboard:
First we need to count along 2 notes, remembering to count the black notes too. So, in this case, we do end up on a black note:
Our "recipe" says we need another 2-note gap next, which takes us to the next black note:
Now just a 1-note gap, taking us to the adjacent white note:
We continue 2-2-2-1:
So we can have a set of bells in any key, as long as we maintain that pattern of gaps (known musically as intervals).
The next issue is that we don't always have 8 bells, but we still want our rounds to sound "finished". That's fine, we just use as much of our "recipe" for an octave as we need. Note that these are the gaps between bells, so for 6 bells, for instance, we have 5 gaps.
For instance, here are the notes for a set of 5 bells, shown on the guitar. Note the 2-2-1-2 pattern of gaps. The star is again the tenor. The 2nd and 3rd are closer in note than any other pair of the bells:
And what if we have more than 8 bells? As we saw right at the top, the pattern on the keyboard repeats every 7 steps. So, counting up from the lowest note, the eighth bell will be another "starred" note and we begin our "recipe" of gaps again from there. So we get:
In fact, on 16 bells, like they have at Birmingham, we've actually gone into the 3rd octave, starting the pattern once again, with that final gap of 2. (Photo by Jonathan Townsend)
Now we know how to arrange a set of bells in a major diatonic scale, what do we do if we haven't got enough ringers? How can we make it sound normal?
The easiest answer is always to ring the back bells, so that final note is always the tenor. That way, you will have a complete scale of however many notes. So on a ring of 8, it sounds much nicer to ring the back six than the front six.
But the back bells tend to be harder to ring, especially in changes on a lower number of bells, so are there any other sets of bells that will sound nice? We will restrict ourselves to sets of consecutive bells for now. We have already seen the gaps needed for a major scale on different numbers of bells, so we need to look for those patterns amongst the pattern on a higher number of bells.
On 8 bells, the front 4 form a major 4 - you can see that 2-2-1 pattern from the table above. This extends to ringing the front 6 on 10 bells. But on 12, the front eight bells have a different spacing to that which we require, although you can ring the front 5. The crucial point is where those gaps of 1 appear in the sequence.
Having a whole octave does sound good, though, so we really would like to be able to do this in a ring of 12. One solution to this is to have an extra bell, to use instead of one of the normal scale.
In the ring of 12 above, we were almost there; it went wrong when we got to the 2nd, as we wanted the pattern of steps to have 2-2-1-2-2-2-1 at the end, rather than the 2-2-1-2-2-1-2 we've got. In order to make that penultimate gap of 2 notes, the 2nd bell needs to be a higher note, known as a "Sharp 2nd". The treble is fine, as it's still 3 steps from the 3rd, although we've changed the 2nd.
Another method to get a lighter ring of 8, used at Great St Mary's, is to have a "Flat 6th". Looking at the gaps on 12, we see the pattern coloured in red is again quite close to what we want:
But we need to make it start 2-2-1-2, rather than 2-2-2-1. And we can do this just by changing one bell.
The 6th bell of the 12 is the one that we want to adjust - it only needs to be one step above the 7th, i.e. a lower note than the normal 6th. So at GSM, they have two ropes falling near each other. To ring all 12, the back 10 or the back 8, they ring the normal 6th, but to ring the lighter 8, they ring the Flat 6th instead. Here Shirley is ringing the 6th, with its normal, maroon rope, while above her head, you can see the striped sally of the Flat 6th, tucked out of the way. (Photo by Anna Sugden)
Some towers, like York Minster or St Mary Redcliffe in Bristol, have not just a Flat 6th, but also an extra treble, to enable a lighter ring of 10.
Now, with towers currently only able to ring a selection of their bells, to enable social distancing, which bells sound best?
We know from ringing Queens that ringing every other bell makes a pleasant pattern. So that's a good start. 1-3-5 or 2-4-6 both sound nice on 6 bells. Finishing on the tenor is generally preferable, but might not be the easiest, if you've got to get the bells up, rung and down in 15 minutes! On 8 bells, you can ring the odd bells or the even bells, but 1-4-6-8 is good musically, as both 1 and 8 are "starred" notes, as we saw above. The only issue might be spacing between treble and tenor, but having a family grouping there could solve this. At Birmingham, they carried that "arpeggio" pattern even further, ringing what they termed their "Magnificent Seven", with the same pattern in the next octave too: 2-5-7-9-12-14-16!
Can we ring more bells, using family groups, or using more widely spaced adjacent pairs of bells? Again, finishing with the tenor is good, either in conjuncton with the penultimate bell, or the antepenultimate one, as you would ringing just the even bells. Ringing 4 of a 6 you could ring 1-2-3-5 or 2-3-5-6. On an 8, it's harder to ring something nice on the lighter bells - how about 1-2-4-6? And it's tricky to get a set of 5 - perhaps 2-3-5-7-8?