So, we’ve talked about the tools you might use to tune and a few approaches to assuring you tune all your strings to particular pitches. But last week, Sara brought up a good point that I had been dancing around.
Why? Because it’s easy, but not simple. What?!
So, let’s start with a caveat. I’m not an expert in tuning or the mathematics and music theory behind tuning. I’ll share what I know but please understand that this will be a skimming of the topic*. Here goes.
The Social Component. You might not have known there’s a social component to tuning, but there is. We use A= 440Hz as we mentioned before. But why? Because this is the current convention. Translation,
“We do it that way because that’s the way we do it.”
In times past A = 432Hz, and who knows what it was before that (ok, someone probably knows, but I don’t). This consensus on what “in tune” means is the social component of tuning – we’ve agreed, we’ve come to consensus that we will use this standard (A = 440Hz) to tune our instruments.
After all, why do we tune at all? Because making music is social – and we want to enjoy playing together.
Having said that, there are other elements of this social consensus. More plainly, there is more than one “tuning system.” These tuning systems “define” the scales you tune to. There are loads of systems, and variants on them, and like every other human endeavor they have grown, developed, and changed (morphed?) over time. Here are the two Temperaments you are most likely to bump into playing the harp. I’m presenting them here as fait accompli but realize that they are all defined through and across music, philosophy, culture, and history.
Equal Temperament. I’ve started here because this is the system you have likely always used (and unless you have changed a setting on your tuner, it’s what most electronic tuners use). This system has the twelve tones that match the keys on the piano (C, C#, D, D#, E, F, F#, G, G#, A, A#, B) and the pitches are distributed equally. This is the tuning that makes it possible for the piano to be played in each major key**. The upside is that everyone can play together. The downside is that when you smush the pitches like that, they are no longer mathematically “correct” and when this was first used, it “sounded funny” (or more likely slightly off because when they did that, the notes all moved a little, sort of like kindergartners shifting around in line for cookies). If you’re not sure, look at your tuner (or at the paperwork) – it likely says it’s equal temperament.
Pythagorean Temperament. You’ve heard of the Pythagorean Theorem? Pythagoras thought that all beauty could be captured in mathematical ratios – the right triangle, the movements of the planets, and the arrangement of pitches. This tuning is based on tuning “pure 5ths”. This is the tuning you might use if you worked with a tuning fork. This is the temperament that is easiest to tune by ear – you listen for the glorious pure 5th (remember – an in-tune 5th will “ring” and be audibly in tune. You can’t miss it – and if you’re not hearing the ringing, you’re not in tune yet). Each pitch will be near its cousin from equal temperament but only the octaves and 5ths will be exactly the same.
There are other Temperament Systems including Meantone, all the variations of Equal Temperament (the 12 tone we’ve talked about above and including a lot of others counting up to 72 tone, Well Temperament (which Bach used to make a set of tunes for all 24 major and minor scales available on the keyboard at the time), Just Intonation (which I’ve never run into but is a thing), and many more. Remember too that the temperament selected might have more to do with the music being played (renaissance had a different sense than modern) or the instrument being played (remember, it’s hard to retain theory that doesn’t apply to you!).
Here’s a suggestion – play around with your tuning and see what you think. If you’re typically using Equal Temperament, try Pythagorean and see what you think. You might make lemon face because, it will be slightly different. It probably will sound out of tune, but if you’re interested, give it a try.
Which type of tuning do you use and why? “Because that’s what I was taught” is a perfectly good answer! Did you try another approach? What did you think? Let me know in the comments.
*If you’re interested, there are many books on tuning, but one of my favorites is Lies My Music Teacher Told Me by Gerald Eskelin. It’s a really fun book, and a short read, weighing in under 175 pages, but it is dense going – and having an interest in math will help. Alternately, you can choose the path many do and stick with the theory you have learned by rote from teachers who have learned by rote. Another way to say that is,
It has always been thus….
You will do fine if you want to keep it there, but read the book if you’ve always wondered.
** if the wording starts to be a little stilted, please note that is me attempting to be correct in an area that I don’t fully understand (nor do purport to), and is language that many musicians have bandied about but is actually quite technical – kind of like you call it a bruise but your physician calls it a hematoma – they’re both right, but one is more technically accurate than the other!
Because I am indeed nerdy about tunings and temperament, I’ve still been thinking about all this and wanted to add one more comment to reinforce some of our teacher’s wisdom: which is, when you’re playing with other people then yes, you need to ensure that however you tune your harp fits with your fellow players both in terms of pitch (A-440 or whatever) and temperament. But when you’re playing for yourself — *you’re* the one and only one you need to please. The machines are just machines….they aren’t “musical” and don’t always make the music sound right. Tune your harp however it sounds best to *you*. You be the judge. Adjust some intervals if they don’t sound “right”. Adjust some differently for different pieces you play. You could even devise your own temperament like so many guys did during the Baroque era and name it after yourself — why not!
I’m not much good at mathematics but I can easily get very nerdy about tunings….as most musicians are who play “early music”…(and my harpsichord is tuned to A=415, which is quite typical, and about a full half-step lower than modern pitch — and BTW most orchestras now are playing well about A=440 as pitch continues it tendency to rise) The reason you can’t tune all in pure intervals on a multi-stringed or a keyboard instrument is that a series of pure thirds ends up being smaller than an octave while a series of pure fourths or fifths end up being larger than an octave. So temperaments are what are used to “spread out” these differences among different intervals so you can play in all or most keys and be mostly in tune. The problem with equal temperament is that all intervals are tempered by the same (equal) amount, meaning *none* of the intervals apart from the octave are pure. This is why even though equal temperament is a very old idea it was not accepted in Germany until about 1800, and in France, England and Spain not until decades later, and only in general worldwide use since about 1900. I have a lovely little booklet that provides diagrams and directions for 15 different termperaments, starting with Pythagoras and ending with Equal. I use one of the many Baroque era tunings for my harpsichord that was devised by student of Bach’s; I chose it largely because it’s very easy to set and sounds quite good in almost all keys. But we have more flexibility with the harp because mostly we (or I at least) don’t play in all that many different keys, so we can afford to tune with more pure fourths, fifths and thirds as we please!
Well said! This is a fascinating topic (if you’re interested) and certainly worth the time to learn about. You also highlight any important element – you can choose any tuning you like when you’re playing solo. It’s only when you’re playing with others that selecting one (and only one) temperament will matter!
i tune in octaves, then check in 4ths . why 4ths? Ago, i watched a pro check tune and i thought she was using 4ths, prob it was 5ths but Then, who knew? so….
sometimes i hear a string being “off”, but strings are strings and even if the tuner is happy, it can still sound funky.
so, sounds like (pun, yes) people have gotten WAY overinterested in tuning! any landing you walk away from… LOL
LoL – yup, tuning can be a rich topic. If you’re interested it’s captivating and if you’re not, it’s simply dense.
Jen, I am going to have to read this a second time after my second cuppa, might even need a third reading. This is pretty heavy stuff for my feeble brain but something ‘rang’ true for me. I can sometimes discern that ring you talked about, even with the diminished hearing (something I discovered fairly recently).
I may have to explore the Pythagorean method – that theorem I could accept without understanding, in high school all those decades ago. I have a tuning fork somewhere….
Barbara – you’re right about that third cup! I have read and reread and rereread this stuff. I knew I was on to something when I finished the reading and had that faint shimmer of understanding (Feynman would have asserted – correctly – that I didn’t know it because I couldn’t have taught it to a primary schooler!), so I go back to it repeatedly. I’m hoping that this week I have given a Feynman worthy representation of understanding it (but probably didn’t!).