Singing Semitones

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night and dayMagenta has been working on my arrangement of Night and Day recently, which has a lot of chromatic movement in the harmony parts (not my fault – Cole Porter wrote it that way). We’ve been tackling this by developing our sense of scale degrees, and the notes between them.

This is all part of my general campaign to encourage people to conceive pitch in terms of tonal context rather than in terms of intervals. I have had a clear rationale for this for some time, but recently had one of those revelatory experiences which made me realise why it was even more important in the case of semitones.

So, the basic reason to think in terms of scale degrees rather than intervals is to avoid the problem of transferred error.

If you are singing by relationship with a tonic, you always have a clear reference point to connect to, whereas if you sing by intervals, each note’s primary reference is the previous one. So, if you get a note wrong, and work by intervals, the next note and all other notes thereafter will be equally wrong until you stop and regroup. But singing relative to a tonic, a wrong note has no further consequences beyond itself: the next one can re-establish its own relationship with the tonic and you can carry on accurately.

There are various side-benefits from this approach. The ensemble develops much better pitch retention if everyone is using an internal sense of key as reference point. And it supports the development of musical literacy.

The semitone revelation came at the hands of David Wright on his recent visit to train and recertify the Music Category judges of the two British barbershop associations. It was one of those wonderful moments where he took information that was sitting inertly in my head and put it together in a way that transformed the way I looked at the world (or at least how I look at semitones).

The context was the tuning of chords, and how singers will tune to just intonation when left to their own devices without the interference of accompanying instruments. That is, they’ll sing intervals in their pure forms rather than in the slightly distorted forms that equal temperament imposes to make keyboards work in all keys. So far so good. The revelatory moment was when he mentioned, just in passing, that a consequence of this is that the semitone is an unstable interval.

Oh yes, I thought, so it is. The semitone between the 3rd and 4th degree of the scale is going be the difference between the 4:5 ratio of the major third and the 3:4 ratio of the perfect fourth, whereas the difference between the augmented fourth and the perfect fifth is going to be the difference between 3:2 and √2:1. (And thanks to Peter Mumford for pointing out to me that dividing the octave equally in half gives you an irrational number.) Semitones, even relative to a single reference point, come in different sizes.

And if the vertical chords are tuned so that the perfect intervals are perfect (as singers will always prefer), then the size of semitone will vary according to how the harmonies require the chromatic notes to fit in. So, the very worst thing we can do is to try to think about singing from one note to the next in half-steps, since we have no way of predicting how big or small those steps need to be.

Singing relative to the tonic is better, since you will always get each note into the right kind of region – the diatonic notes will sit quite stably and the chromatic notes can slot in between. But we’ll only locate exactly where to slot them in between if we also listen vertically to the harmony as well.

This is about musicianship – and interestingly lets us define different levels of musicianship according to how much of the surrounding musical context we pay attention to:

  • Lowest level. Paying attention to your own line only (and indeed, to the previous note in your own line as primary means to find the next note).
  • Middle level. Paying attention to your line in relationship to the tonal centre
  • Highest level. Paying attention to the whole music in relationship to the tonal centre.

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