Category: spectralism

Microtonality is the use of intervals smaller than a half-step such as quarter tones, sixth tones, eighth tones and so on.

There are several standard ways in which microtones are used (which may be interconnected):
• As part of a “just” intonation scheme (based on pure intervals instead of equal [keyboard] temperment). Used in a simple way (also known as mean-tone tuning), one plays perfectly in tune in a given key, less so in related keys and totally “out there” in remote keys. So far I have come across no better explanation and description for just intonation than David Doty’s Just Intonation Primer. Or click here for an on-line explanation of just intonation.
• As part of a “spectral” scheme where the notes are not tuned according to equal [keyboard] temperment, but according to the intonation of upper partials of a given overtone sequence. This is related to just intonation (and again David Doty’s book explains this wonderfully), however in a “just”intonation environment there may be a tonality implied, whereas in “spectral” music a tonality is rarely implied (although there may be a tonal center). Here is an example of how the overtone sequence on our low C is naturally (purely) tuned. The deviation from equal temperment is measured in cents. (Cents are measured by dividing an equal tempered half tone into 100 units. These are marked on most tuners to indicate the degree to which one is sharp or flat.)
◦ 1st harmonic (fundamental): C (no change)
◦ 2nd harmonic C (no change)
◦ 3rd harmonic G: (2 cents sharp)
◦ 4th harmonic C: (no change)
◦ 5th harmonic E: (14 cents flat)
◦ 6th harmonic G: (2 cents sharp)
◦ 7th harmonic Bb (31 cents flat)
◦ 8th harmonic C (no change)
◦ 9th harmonic D (4 cents sharp)
For the deviation up to the 31st harmonic, see Wikipedia’s entry on the Harmonic Spectrum.
For tips on how to get these partials in tune without having to resort to watching the cent meter on your tuner (i.e. by ear) read my entry on spectralism.

• Sometimes a composer may invent a tuning system, then it is up to you to determine: a) why/how the composer uses microtones and b) how you should approach them. These questions will help to determine whether or not the composer has included microtones as special “effect”; i.e., should the “de-tuned” notes be given special colors to contrast the “normal” notes, or does the composer want consistency of timbre? This is an important factor in determining fingering (if not already prescribed by the composer).

Once the interpretive questions have been addressed, there comes the time to actually play them. There are several fingering charts available such as Matts Möller’s quarter-tone chart. They are good resources but think of them as starting points. My personal advice is to know as many fingerings as possible for a particular note. Be flexible in the choice of fingering because there are several factors to consider when making your choice:
• the speed of the gesture
• the intervallic relationship to its neighboring notes
• the dynamic and tone color
Although each of these is an important consideration, it is crucial to know your end tempo and always have it in mind. I have made the mistake of carefully going through a score and writing in all the “correct” fingerings for microtones, only to have to change them later as I got the piece up to tempo. Practice the notes in tempo, if only two or three at a time to get a feel for this.

Sometimes the solution can be simpler than you think. Turning the flute in or out to “de-tune” a note can work just as well as a really complicated fingering. For example: on a standard flute there is no stable fingering for F 3/4 sharp. If you need a loud, stable tone just play F# and lip up. If you need a quiet clear tone, finger G and lip down. (Of course if you want that hollow, bamboo sound, use low B and half hole the F-key [index finger right hand].)

A note on different flute models: I play on a quarter-tone Kingma System (produced by Osten-Brannen). This is a really great system, and I can recommend it for anyone who wants to play a lot of contemporary music. These flutes are also suitable for all repertoire. However, every flute has the capacity to play microtonally (as we all know, sometimes inadvertently!). Please don’t be discouraged from playing the modern repertoire if you have a standard flute, even if you only have a student model with closed holes. There is still repertoire that can be played on student models such as the flute solos by Karlheinz Stockhausen. See my repertoire list for more suggestions.

Some days ago I got the score for G. F. Haas’ new work „ … wie Stille brannte das Licht“. (What is it with German-speaking composers and their titles with elipses?). It got me thinking about how different composers notate microtonality. I like what Haas has done, it is explicit in placing the note within a frame of reference.

The notated C quarter-sharp in bar 241 is the 11th partial of G, and the A-flat in bar 245 is the 21st partial of E-flat (along with the indication that you are in a perfect fifth with the clarinet). I like having this kind of information in the score, but if he had notated the exact deviation in cents, that would have been even more helpful. This is easy enough to find out in Wiki

That 11th partial should a C# 49 cents flat, and the 21st partial should be an A-flat 29 cents flat. Like I said, easy enough for find out, but it would have been nice if the composer had provided this information.

We haven’t had rehearsal yet, so I can’t say how this will sound or how easy this will be to hear. [ed. read my follow up at the bottom of this post]
So now the question arises: How does one practice this stuff?

First of all, I get my tuner. Trying the A-flat first, I make sure that our Eb’s are in tune. Then I play an A-flat ca. 29 cents flat. Then I keep that tone while putting the sound on to Eb and I hear a Bb combination tone. This is a clue that I am on the right track, or within the correct overtone spectrum. Your combination tone (it may be a true difference tone or not, depending on the timbre and register of instrument) should lie in close relationship to the fundamental – say an octave, fifth or major third (which is the 5th partial, you don’t want to go much farther than that). Put in simpler terms, it should be part of the major triad formed by the fundamental.

Now to try the C# against the G. Again I tune the G’s, then test my C3 so the needle goes about 49 cents flat, then put the sound on G. My difference tone is B natural this time, still close enough (a major third – the 5th partial) in relation to G to be correct.

Again, I have no idea how this will work in the context of the piece, or if it will be heard. But now I know, theoretically, how much adjustment is “correct”.

Whether this works in context or not, I love working with combination tones. Scientists are still not in agreement as to what they are – but it is a wonderful example of how our brains work – how they “fill in the blanks” of the overtone spectrum. I wonder if this is the same phenomenon that allows transistor radios to work? Only the upper partials are projected, the brain fills in the rest.

Also, I’ve noticed that I’m one of those people who can read things like this, hence my spelling problems, most likely. (Thanks to my like-minded Uncle T for this text):

fi yuo cna raed tihs, yuo hvae a sgtrane mnid too. Cna yuo raed tihs? Olny 55 plepoe out of 100 can.

[Follow-up added May 5, 2009]
The passage in question was actually not so difficult to hear! You are a part of this “lump” of sounds that are related to the fundamental. It is tricky that he has two harmonic spectrums going at once: those of G and E-flat.

When considering dynamics in this piece we realized that there was a lot more going on than just playing loudly or softly. It helped to think of crescendo/decrescendo passages as adding/subtracting harmonics to your individual sound rather than just making the sound louder or softer. This made for a much more interesting color. Also, the very quiet passages must be played with focus and good attack. Even the quietest notes need some harmonics in the sound, none of this fluffy airy stuff! It just didn’t match the color system.

I do admit the 11th partial gave me the most trouble in this piece. Tricky to hear! It must be 49 cents flat. I must make some exercises.

Speaking of which, I asked the composer and my colleagues how one can study and practice this music. The answer is always the same, learn the overtone series, horizontally, note by note, by ear. How can one do this? Programming a synthesizer seems to be the most popular idea. However you do it, once the sounds are in your head, you have to find a way to play them (of course, in a comfortable range of your instrument. I’m thinking middle octave) by using a combination of alternate fingerings and lip bending. Another project for me!