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Posted by on Sep 10, 2013 in Background, Equal Temperament, Just Intonation, Recordings, Septimal Harmony, The Lattice | 2 comments

Premature Nostalgia: Making Friends With Equal Temperament

I just recorded a new song, and it’s a perfect example of how equal temperament and just intonation can get along together.

Here’s the cut:


Reading this blog might give you the impression that I’m “against” equal temperament and “for” just intonation, or untempered music.

True, discovering untempered music has been like sailing to a new world. It’s delicious to have 20 or more notes to work with instead of 12, each with its own individual personality.

Equal temperament, however, is a fabulous invention. The lattice of fifths and thirds does not quite repeat. If you start with any note and go in any direction, you will soon encounter almost the same note again, but it will be off by a comma, a small interval, from the original note.

There are no two notes tuned exactly alike on the entire infinite lattice.

Equal temperament flattens out the lattice just a hair so it does repeat. Now there are only twelve notes to work with, and they imply the untempered ones in the ear. This innovation makes lots of things possible in music. Beethoven and Mozart could not exist without it.

It’s sometimes said that equal temperament and just intonation are incompatible with each other, because the notes will be out of tune. I say they can get along fine, you just have to show ’em who’s boss.

I submit for your consideration: Ray Charles.

Ray Charles’ piano is an equal tempered instrument. Ray Charles’ voice is most certainly not. He is singing the exact resonant notes, those blue notes, all tuned just like a gospel choir, which is what he grew up loving. Ray is boss. His voice establishes the tonality of the song. The backup singers, the horns and the standup bass all agree, this song is in the harmonic pocket, and it resonates.

That leaves the piano slightly out of tune, but who cares?

Notes that are slightly out of tune don’t necessarily sound bad — that’s the basis of the “chorus effect.” No two singers in a choir are exactly in tune with each other, and the resulting complexity is a huge part of the sound of the choir.

So if the tonality is established in the ear, maybe the equal tempered notes, which are only a bit off after all, will just enrich the sound a bit.

Listen to how “Hit the Road, Jack” starts off. First the piano intro. ET. Then the horns kick in, and they start to establish the soul of the tune. Then come the backup singers, that gospel choir. When Ray’s voice finally joins them, the pocket is waiting for him, and he proceeds to own it. The piano is now a background instrument.

I think that’s the secret. Put untempered instruments up front, and ET instruments more in the background. This asserts the untempered tonality in the ear.

Playing acoustic guitar and singing is a great playground for this. The acoustic guitar is, in its bones, an equally tempered instrument. Fretted instruments drove the adoption of ET in Europe, even before keyboards did. The voice is the archetypal untempered instrument. It can do anything.

If the guitar is boss, the song will be in equal temperament. If the voice is boss, you can establish any tonality you want (blues, Gypsy, whatever), and the guitar will tag along. You can retune it in the ear, just like Ray retunes his piano.

Here are some tricks for making friends with acoustic guitar (or any tempered instrument):

1) Sing solidly in tune, with the tonality coming from you, and not from the guitar. Don’t follow the guitar, lead it. The song is the melody, it is your voice, and you are accompanying that voice with guitar notes.

I like to think of the guitar as playing the grid lines on the map. The guitar notes are perfectly equally spaced, and are excellent reference points. The guitar tells me where I am. We completely agree on one note, the tonic. I use the tonic on the guitar as my true home base.

My voice is playing the actual territory.

2) Sing louder than the guitar.

This isn’t all that easy. The guitar is projecting outward, so it sounds louder to the audience than it does to me. The voice is right there in my head, so it sounds quieter to the audience than it does to me. If I sound balanced to myself, the audience will hear way more guitar than vocal. I hear this all the time at open mics.

I’ve found that in an acoustic setting, I have to sing twice as loud as my guitar (from my own point of view) for it to sound balanced out in front of me.

It gets easier with more JI instruments. In “Premature Nostalgia,” the fretless bass and backing vocals are all in strict just intonation. The guitar is truly a backing instrument, and the tonality of the song feels secure.

3) There is a third, more subtle thing you can do to bring the guitar closer to just intonation. The most clearly out-of-tune note on acoustic guitar is the major third. It’s already 14 cents sharp even when perfectly tuned, and the slightest unintentional string bend will take it into some really grating territory. Choose chord voicings that de-emphasize major thirds, and your guitar will sound a lot sweeter. I wrote an article illustrating this effect, here.


  1. Hi Gary,

    Thanks for making such great effort in passing your vision to the audience and sharing your insights!

    Being engaged in similar conceptual spaces, may I comment on this particular article.

    While it’s definitely practical to think of the equal temperament as approximating an (‘over-‘ or ‘underlaying) just-intoned tonality, it’s worth making a point about the concept of ‘tonality color’ that is essential to any meantone temperament while is totally absent in the equally tempered instruments. (This refers to the following article by Kyle Gann: ‘An Introduction to Historical Tunings’.)

    This makes me wondering about the following. How much the idea of tonal distance (that is, having a natural hierarchy of more or less remote tonal areas, or regions, around an arbitrary tonal center) is applicable to composing within an equal temperament idiom?

    Would you agree that being concerned with the equally tempered composition, the distance between tonal areas only introduces itself by how smoothly the two regions are connected? I.e., providing a smooth, step-by-step, voice leading is more essential to embrace a ‘natural’ modulation within an equally tempered harmony, than it is within justly intoned tonality where it makes more sense to move across the tonal regions that are most closely related by their overtonal content (even if such moves require jumps in voice leading).

    In turn, this makes for another equally-tempered feature: the possibility to trick an ear to perceive virtually any tonal area as the center (the main, the starting one). And once a smooth voice leading is figured out, the overall tendency for the composition appears to continue traversing though the entire set of available tonalities, by cycles. At least, there’s no natural closure to such move. (This refers to the practice of ‘modulating to a dominant’.)

    I am eager to hear your valued opinion about this.

    Kind regards,

  2. Hi Yuri.

    Nice point about meantone tunings. In these systems, playing in multiple keys is possible, but a piece will sound subtly different in different keys, an effect which I imagine composers took into account and which is now pretty much lost. Remember Nigel Tufnel’s comment in Spinal Tap that D minor is the “saddest of all keys”? In equal temperament that’s a good joke, but in meantone it might actually make some sense.

    I’m not quite clear on your question about voice leading. Are you suggesting that in JI, it’s smoothest to make small steps in harmonic space, while in ET it’s smoothest to make small steps in melodic space? I would say that melodies and the individual voices, “want” to move by small melodic distances, and that the overall harmonic structure (roots and triads) “want” to move by small distances on the lattice, that is, in harmonic space.

    To my ear, large, non-sequitur harmonic jumps on the lattice are equally jarring in ET and JI. However, ET allows moves that are not really available in JI, most especially a “comma zap,” in which the harmony teleports from one location on the lattice to another location a comma away.

    ET “folds” the lattice so that all commas are eliminated. In JI, the 2 and the 2- are a long ways away from each other. In ET, they are right on top of each other, and your chord progression can exit through the west door (the 2-) and reenter through the east door (the 2), like Magellan sailing west and winding up back where he started.

    Mathieu’s book might really float your boat.

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