Saturday, April 02, 2011

Intonation Game

I just came across an interesting intonation game that offers electronically-generated pitches and asks you to determine whether they are too high, too low, or just right. I wonder if these pitches were generated acoustically, on an actual violin, if it would be as easy to tell whether they matched. I also wonder if it is even possible to sustain an exact pitch on a stringed instrument, microtonal or otherwise, for more than a fraction of a second, since acoustic sound waves are living and moving entities.

This brings up my previous thoughts about the actual ability for anyone to truly play microtonal music accurately.

Related posts:

Bohlen Pierce Scale
Microtonal Ramble
Lend Me Your Ears

Nobody has answered the question I asked at the end of the Bohlen-Pierce Scale post.
Can anyone (who doesn't have perfect pitch) explain how a person with only a western musical background could sing microtonal or alternative-scale music accurately.
I'm still waiting!


Prent Rodgers said...

Perhaps I don't understand your challenge, when you ask: "Can anyone ... explain how a person with only a western musical background could sing microtonal or alternative-scale music accurately." I could just as easily ask how a person with no medical training could perform open-heart surgery, or someone who doesn't know the violin play first chair in the Philharmonic. Why would you expect someone with no training to perform at an expert level?

Elaine Fine said...


It isn't a challenge. I really want to know! The reason I specify a Western music background is that there are scale systems in Middle Eastern and Far Eastern cultures that would not serve as points of reference for me as a person brought up in the Western musical system of diatonic music made of half steps and whole steps.

I'm posing this question to performing musicians who specialize in microtonal music and composing musicians who write microtonal music.

David Kulma said...

Lots and lots of work, using pitch references, drones, repetition, as we do with 12 tone equal tempered music. It is just asking you to have a more discerning ear, which is learnable. We can only sing in 12TET, because we practice for years. Western music's tuning system isn't any more "natural" than any other, it is just what was passed down.

It seems you believe that putting in this amount of work is ludicrous, as being able to play in tune and discern the pitches in music you already play takes a lot of effort.

I personally can hear the notes and their differences in Ben Johnston's music, and believe with practice, I could replicate the results.

Elaine Fine said...


What leads you to believe that I think putting work into playing microtonal music is ludicrous? What I want to know is HOW you go about using your ear to "check" yourself when playing microtones. I want to know how, if given a sample acoustic pitch, you could sing or play a pitch on an acoustic instrument that is exactly a quarter tone higher or lower, and replicate the process. I imagine that on a stringed instrument it would be possible to judge pitches relative to the open strings, and on the violin, which has natural fingertip-width half steps, by the physical distance (unless reaching the pitch in question is a leap). I imagine that it would be more difficult on the cello.

I believe that the musicians of the Kepler Quartet do it accurately, but I really can't tell you for sure if what they are playing truly represents the correct divisions of the octave. If I were asked to judge whether they were playing Ben Johnston's music in tune or out of tune, I would not be able to report with honesty.

I don't think that playing microtonal music is a question of having a more or less discerning ear, since in diatonic music we are constantly adjusting our pitches to play "in tune." I suppose that you could say that string players use "adjust intonation." It's a question of finding a technique that works dependably enough so that the intentions of a composer who works with microtones are replicated.

Please let me know, after you have practiced (and on an acoustic instrument or a voice) how you achieved accurate microtones!

I know that Milton Babbitt could hear everything, and he could let people know when something wasn't right. He's not alive anymore, so we lost the source. Johnston is alive, and I imagine that he can hear (perhaps not replicate, but hear) where he wants the pitches to be, but he won't be around forever.

Daniel Wolf said...


The musician trained only in 12 tone equal temperament still has some very useful tools for learning to hear and play alternative tunings. The first is simply using comparisons to 12tet intervals: for example, learning to play quarter tone intervals as the neutral position between major and minor thirds, then sixths, and then, eventually, seconds and sevenths. The second tool is in the alternative tuning we work with (and against, as the case may be)) all the time anyways — the natural harmonics of stringed instruments, the partial tones of brass, the overtones of singers. These are the basic building blocks of just intonation and good musicians are already well-aware of the differences between the intervals found in these and the intervals in 12tet in terms of both melodic interval size and harmonic quality. Finally, the practice of musicians in adjusting intonation through the elimination of inteference beats is yet another way into and for optimizing performance in alternative tunings.

Elaine Fine said...

Thanks Daniel. What about smaller divisions than quarter tones? I like the neutral position idea (which I'm excited to try), but it still seems like it might be inexact when dividing an octave into more than 24 quarter tones.

I suppose it is actually listening FOR beats rather than trying to eliminate them that is the name of the game.

Chance said...

It's honestly easy to hear and tune to some microtonal pitches, especially ones that are just ratios that fit into a pocket of sound where there is minimal interference in the overtones produced - harmony based on lower limit just ratios is easy to hear and replicate - easier than any equal temperament, edo, or false tuning systems that use arbitrary methods to calculate long iterated numbers like the 12^1/2 tuning method that is inexact and falsely given as our "permanent" choice for tuning problems to be swept into inexactitudes and pseudo-pythagorean adjustments.
If you take a 5/4 for instance as the starting point for developing scales and chords, as well add the 3/2 as a perfect consonance that is easy to sing, hear, and adjust to, maximally the ratios combine to produce wonderful consonances, even higher limit chord-spectrums can be achieved thru listening carefully - to the beating affects of wave vibrations in combination, and also to the tones themselves and how they fit, or pocket together. Miniscule differences can be heard in color-tone choices between, say, a 5/4 and it's neighbors that pool outward into close relationals that also sound similar to what we perceive as a major third, the just major third of the 5-limit variety offers a beautiful consonance that is easily heard as correct, but there are other tones nearby that can be heard as affectual, brilliant, somber, classically high or low compared to that starting point... as the tones become more complex they become more jarring, but instantly distinguishable to someone who has trained their ears toward the differences, optionable qualities of tones nearby the main chord-tone choices become easy to hear, easily recognizable as in-tune consonances that would inspire us to use our palette more brilliantly into a future dressed in microtonal consonances that spark our ears to listen harder, play more brilliantly, sweep away our mistakes of choices of tone no longer into a future reified into 12 notes unadjustably mistaken of themselves, each interval is like a pocket of tones that hit the mark and warble exactly so into the air, producing vibrance and brilliance as they eminate toward our ears, how we hear them all is unique to our culture and upbringing, but not so that we'd not be able to distinguish say the difference between an 81/80, a unison 1/1 consonance, a 125/128,(multiplied by any starting tone, etc.) or between the septimal tones and their close neighbors, 225/224 splits can be used almost anywhere to produce 5-limit tones, or instead their 224/225 semptimal limit neighbors, so too can tones be used with their close microtonal neighbors like 99/100 of any tone on your keyboard, either as an optional pitched difference-tone that gives unique color to a scale, or in place of one or the other to switch out a tone for another close by, to give a melody a certain edge (in a way that singers do all the time, mostly unconsciously - but with intent too, sometimes). All tones are good? Maybe not at all, but some that fit into a spectrum together and are limited to exact tone-choices, exact tone choices that fit together harmoniously, bound by rules - and adjustments to rules, that govern a logics based framework of harmonious interactions of notes and sounds, and even exact considerations of vibrato, timbre-control, etc... choices built upon logics and considerations of exactitudes of pitch-relations that intersect into mathematical diagram-based attenuations to the heart of our own hearing & psyche-based understanding of what is good... Quality, in a nutshell, can be described as an intersection of these understandings, mathematical but also framed in conjunction with our own cultural understandings of self, our own attenuations to soulfulness, and what it means to be alive.

Elaine Fine said...

But how do you sing them (i.e. generate them without the help of a device, electronic or otherwise)? What I can understand of this explanation seems to be a an appreciation of microtones, but not a way of producing them in as sure a way as musicians can produce half steps and whole steps.

Chance said...

meant to say: "...2^(1/12) tuning method that is inexact and falsely given as our "permanent" choice for tuning problems to be swept into inexactitudes and pseudo-pythagorean adjustments."

Chance said...

You can approximate each interval by listening and playing whatever instrument or voice - using drones, or chords produced with synthesizers that are tuned microtonally. To get the tones exact on a synthesizer, one can use Pure Data, or Max/Msp or Native Instrument vst synths, or whatever microtuning programs available to you.
But then, it's also possible to do this::
Sing with yourself, overlayered and recorded onto a computer, or field recording device - play instruments that are tunable, flexible, etc. and play freely, but adjust things to hearing and playing what comes to you, use intuition, guidance, however you call it when it happens on its own. When you train in this way it produces brilliance that is sometimes beyond what you'd expect, whatever limits the composer, whatever there is that is culturally embedded may get in the way of your perception of goodness or quality... this practice can produce works that are beyond what is usually heard in this time period... What I mean is if you let go into it non-judgmentally, completely secure in letting each pitch come to you before you move to it - allow the voice to move thru you, it can create layers and layers of densely coded musics that are beyond genres of today, even if they hint at or suggest genre at any time-point.

Sometimes playing in this method can be freeformed where someone has their own initiative and moves to or away from a pitch based on their own perception of what is right... to do it honestly, it takes relaxation and utmost precision of patience where you let go of all desire to hit this/that note, everything comes to you as you wait for it - all motion. It's a practice in stillness, but I pass it on to you, if you're ready go for it. But be patient, when it arises full-forced it's a beautiful way of being creative.

Chance said...

Here's a disc I made with that method - (but it's not perfect, in its timbre it's good enough, but the mastering was incomplete, time crunch happened etc. ...if you play it in itunes you can use the equalizer function to eq it up a bit brighter, and louder so you can hear the subtleties...)

It's different, lush and beautiful in its own way. Not exactly what I'm going for nowadays - more culturally bound and beautiful in a radio-song way for my newer pieces and discs, but in some ways I like to break barriers of what is heard as possible in music, strive for things beyond the norm - and this disc has a lot of microtonal interplay...


Music Crazy said...

Depends what you mean by microtonality. Twelve equal is relatively new. Even Chopin didn't use twelve equal, he used a temperament. So in that sense all cultures have used microtonal music. The reason is that twelve equal is a compromise temperament which is ideal if you want to modulate to any key and they all sound the same. But none of the intervals in it are pure ratios. The fifth is a bit flat, not noticeably so but you get beats in long held chords. The major third is sharp, quite a bit, compared to the harmonic series major third. The minor third is flat.

In Western music, early music was basically pythagorean, chains of pure fifths (ratio of frequencies 3/2) which is close to twelve equal.

Later on, it went through an experimental phase with Vicentino's

Bach's "well tempered Klavier" is written for a tempered twelve tone scale, not twelve equal (though for practical reasons lutes in his day and guitars were fretted in twelve equal) - they thought they sounded better.

So microtonal enthusiasts can get keen on exploring the various temperaments of twelve tone tunings.

Anyway so apart from that, there's also modern microtonal music. If you want to listen to it, there's a long list of present day microtonal composers here

xenharmonic (microtonal wiki) - MicrotonalListeningList

(though some of the links may be out of date).

Apart from that some of the main strands are, in no particular order (this will be a bit random, just to give a taste):

Indonesian gamelan music - each "gamelan" is a uniquely tuned orchestra of mainly gongs and other percussion, strings, woodwind, but the interesting thing is each village has its own gamelan and each one is tuned differently. In a way there are as many tunings as there are gamelans, though certain common principles.

Indian music - Indian musical instruments is usually played with a drone, which highlights tiny differences in pitch so they have a lot of sensitivity to minute inflections of pitch.

Maqam music (e.g. Turkey, Iraq) - the tuning is based on a structure of two four note scales a whole tone apart - our seven note system for the white keys is just one example of this pattern - it dates back to Greek times which they developed one way while "western music" developed it another way

Many others
Basically just about any musical culture has probably developed its own tunings.

Just to give a first impression of the diversity out there.

Elaine Fine said...

Thank you, Music Crazy, for this long and informative comment. I am, however, still waiting for someone who can hear and accurately reproduce microtones with his or her voice to offer ways of learning to do this for those of us who are unable to do so. I believe that most people, when playing music that is not based on a tempered western scale, can adjust to the schema of pitches, at least when playing an instrument that has flexibility with pitch (violin, viola, cello, bass), can work his or her way into the musical landscape. But when it comes to demonstrating microtones vocally (not "a little bit sharp" or "a little bit flat," but an exact measurement like a quarter tone or smaller, I still have no idea how it is possible to produce accurate pitches and recognize their accuracy.