Intonation Theory

September 30, 2008 at 03:50 AM · Today when I was practicing I discovered that the entire basis for good intonation -- at least for me -- is the understanding of intervals: half steps, thirds, fourths, etc.

What does everybody here think about this?

Replies (31)

September 30, 2008 at 03:57 AM · Greetings,

your on the right lines. Many people find that when they think they relationship between notes as intervals their intonation improves substantially.

Is this what you meant?

Cheers,

Buri

September 30, 2008 at 01:53 PM · This is a can of worms. This discussion is destined to degenerate into a tempered vs. perfect argument. But yes, whether you are tempering your intervals or not, that is the basis of the scale, the mathematical (harmonic)relationship between vibration frequencies is what is perceived by our ears as in-tune.

Perfect scale sounds amazing, but has problems when one starts modulating, it become very complex and untenable to maintain good sounding intonation in modern music. The tempered piano tuning is the fundmental basis for intonation today. My teacher at Juilliard once asked me when I questioned this - "what else could it possibly be? - and to be sure, no good alternative answer exists, If you play with a piano or any fixed tuning instrument and don't play tempered, YOU will sound out of tune. The wonderful thing about the unfetted strings instruments is that we can push the tempered tuning toward perfect at times and thus get a really vibrant sound - wonderful leading tones and really ugly dissonances, which makes it like the human voice, capable of better that 'perfectly' in-tune in the hands of a truly skilled player. (after hearing such a perormance, a piano sound a bit dull). The great string quartets use this all time in chordal passages to make the chords really shine as they push them towards perfect. Start with a really well tuned piano and learn these intervals. If you really get your mind around hearing the scale and it's intervals, various pitches in the scale framework will start to take on a very distinct 'color.' SOme peopel with very strong perfect pitch have described it to me as pitches being as distinct to them as visual colors are to you and me - identifying an A woudl be as clear as identifying the color red. Only after mastering the tempered scale should you experiment in pushing it toward perfect and when this can be done.

September 30, 2008 at 09:30 PM · Understanding intervals is the first half of the equation. The second is understanding how the violin, and yours in particular, sounds when it's in tune. Strings instruments are peculiar in that each note has its own unique timbre. Regardless of what tuning system you use (or think you're using), any notes that relate to the open strings must ring. If you match another instrument like a piano but the notes aren't ringing, the fact that you're matching will not matter--it will still sound out of tune (or more accurately, out of timbre). No other instruments have this issue.

September 30, 2008 at 10:33 PM · Greetings,

I love seeing this pointed out. Its so fundamental. Thanks Scott.

Cheers,

Buri

October 1, 2008 at 02:29 PM · Once during a chamber work for violin, viola, cello and piano, there was a spot where the three strings had a unison B natural (the cadence was to eventually resolve to C major) , the three strings played the B natural with plenty of vibrato in crescendo and the piano continued solo in C major. The piano was quite noticeably low in comparison and the ensemble broke up in laughter.

We told the pianist to squeeze the piano and bring up the pitch. Then someone suggested that a hair dryer would tighten up the piano strings. Another kibitzer then suggested that we keep a metal meter stick handy to shorten the piano strings; Then a blow torch to heat up the bronze frame.

We then replayed the section, with the string section behaving themselves, and tempering the pitches leading up to C major.

Ted Kruzich

October 1, 2008 at 07:55 PM · Yes, some notes can be tempered. But which ones in C can be besides the leading tone?

October 1, 2008 at 10:12 PM · Greetings,

Ted, thats the real challenge of piano trios- when to play in tune and when to play with the piano;) When your playing somethign really unison like the Beethoven c minor trio and the piano is slightly out you have to get to the rehearsal room real early and get used to the distortions. No extra cash though...

Cheers,

Buri

October 2, 2008 at 10:03 PM · just diatonic tuning is what sounds best to human ears with string instruments. this is because the overtones line up

minor thirds should be 16 cents higher equal tempered

major thirds should be 14 cents lower

etc

check out this article

http://www.soundpostonline.com/archive/summer2002/page6.htm

this is how and why harpichords are tuned they way they are. they are more in tune than piano in most keys.

there are some famous conductors who can't stand the sound of piano because it is so out of tune...interesting

October 2, 2008 at 10:10 PM · Intonation that sounds right in a scale passage is often uncomfortable in chords. Players in string quartets have to tune their intonation to the common chord, which may vary depending upon the key and the chord.

As for the rest - well -- there are whole books about that.

Andy

October 2, 2008 at 10:51 PM · andrew, you are distinguishing between expressive intonation (play leading tones higher, m3 lower, M3 higher) and Just diatonic (opposite, which is necessary to tune chords correctly).

October 3, 2008 at 04:47 AM · While we are at it -- again -- a question. A leading tone, say b in C major, often functions as a third in the dominant (g) chord preceding the solution to c. As a major third, one wants to play it lower than an equally-tempered b would be, but as a leading tone, many play it higher; what do you think?

October 3, 2008 at 04:59 AM · Greetings,

I don`t think everyone plays their thirds that low anyway but its an interesitng question. For me it is answered a smuch by the period of the music the character of the piece and who one is playign wuith rather than by tghe application of a theory.

Cheer,s

Buri

October 3, 2008 at 12:43 PM ·

October 3, 2008 at 02:14 PM · Here's something I've always wondered, since no one in my line of teachers ever used the term "cents" in regards to intonation, how much is a "cent" when you're using your ears? Is it any different than a "smidge"?

My mother refers to "cents" once in a while--she's a piano tuner, but I can never get a good explanation of how much that is.

Anyway, it's refreshing to read this thread--in my line of work, teaching public middle school orchestra students, a great deal of kids can't even match a pitch, and are often confused (even after four years of playing) about which way to move their fingers to simply make a pitch higher or lower.

October 3, 2008 at 10:20 PM · 1200 cents are equal to one octave — a frequency ratio of 2:1 — and an equally tempered semitone (the interval between two adjacent piano keys) is equal to 100 cents. This means that a cent is precisely equal to 21/1200, the 1200th root of 2, which is approximately 1.0005777895065548592967925757932, or about \tfrac{1}{17.3} of one percent.

Thus spake Wikipedia.

Or a "cent" is 1% of the frequency difference between two adjacent semitones. Pretty much the same as dollars and cents in US currency - 1% no matter how the monetary value fluctuates.

Andy

October 4, 2008 at 06:40 AM · And there are twelve semitones to an octave -- rather like the old British money!

October 5, 2008 at 07:12 AM · And twenty octaves make a million. If British money could only do that...

Over the last days I paid attention to those thirds/sevenths. There is at least one occasion where I found I like it low, in tune with the dominant, and do my best to play it that way myself: the c#'' in bar 49 of the Corrente in Bach's d minor Partita. That's: baroque period, and playing with nobody else.

Opinions/preferences, anyone?

October 5, 2008 at 07:40 AM · The tonality in bar 49 is dominant, so it's not surprising you like it in tune with the rest of the chord, eh?

October 5, 2008 at 08:55 AM · No: to me, it's surprising that the high-leading-tone crowd exists. But then, it's surprises we learn from.

October 5, 2008 at 10:12 AM · If you want music, decide how you want it to sound. If you want pitches, decide what each pitch should be :)

October 7, 2008 at 05:55 AM · Look at this thread for the other side of the coin.

All this ratios-of-small-numbers intonation does make for a certain blandness.

I once attended a lecture -- by Otto Frisch, the nuclear scientist -- about music and physics. He demonstrated the 31 tone temperament: even the sevenths were consonant. Weird!

October 7, 2008 at 07:17 AM · The high 7ths and low 2nds like Marina was talking about in that thread, I always think that when someone first hears about it they're going to treat it like beginners treat dynamics - it says p here so you get quiet, and f here so you get loud, but sort of all by itself... Tonight I went to a coffee shop where that have an open mic on Monday night. I go there to kill Monday night sometimes. I was talking to a kid there I know and I noticed a violinist so I asked who he was and the kid said oh, he's playing with us. He was noodling and warming up and he had a great sound, really smooth. His sound had people really captivated, e.g. they were laughing at his unfunny jokes. He was kicked back on a couch with his feet on a table :) Then they went up and he improvised some slightly gypsy stuff behind their slightly country stuff. It was entertaining. The kids get together and jam and so form these ad hoc groups that they take on the road for one night only :)

October 7, 2008 at 08:47 PM · Bart:

I in fact posted that other thread, to see what the other opinion was!

Giancarlo

October 8, 2008 at 05:08 PM · Later I found out the guy was playing a violin by this maker, made in 2005. Worth looking into. For real.

http://www.enquirer.com/editions/2000/08/27/loc_stradivarius_no.html

October 8, 2008 at 07:39 PM · Giancarlo,

thanks for both threads.

Jim,

I could do with a prune or two!

Bart

October 9, 2008 at 08:42 AM · Oh Bart, it's so funny that you mention that particular C #. As soon as I read that, I knew exactly which one you were talking about (as a matter of fact, I can hear it now). I was playing it last Friday at the coffee shop, and I believe I chose it one way the first time through, and then the other way the second time through. Both times, they just sounded confused, though I didn't take the time to think about why, or what I could do to work it out. I was just playing what came to mind each time. Neither way seemed any good.

October 9, 2008 at 03:02 PM · diabolus in musica, Emily!

October 10, 2008 at 09:26 PM · Performing the high leading tone is a common practice of singers who quite often do a slow glissando from this high seventh up to the tonic. It must be an inherent tendency of vocalists who really want to emphasize smoothness.

The unfretted strings, brass and woodwind instruments have no problem in imitating this vocal technique.

However, when the 7th is used differently, as in an ascending passage or as part of an embellishment, it is performed lower.

The tempered scale was a tuning system which was invented for practical reasons since the re-tuning of a piano, harp or organ, to any specific key, would have been impossible during any performance.

Ted Kruzich

October 11, 2008 at 03:39 AM · D Kurganov

Interesting observation on conductors who can't stand the sound of a piano because of tempered tuning. What do these conductors do about the orchestra? Wind tuning is almost always tempered(whn it is even in tune) and string tuning is well a dog's mess.

The other night a heard a 1930's recording of the Brahms 4th Symphony with Dresden Staatskapelle. That orchestra played in tune like nothing on can hear today.

October 11, 2008 at 09:50 AM · "While we are at it -- again -- a question. A leading tone, say b in C major, often functions as a third in the dominant (g) chord preceding the solution to c. As a major third, one wants to play it lower than an equally-tempered b would be, but as a leading tone, many play it higher; what do you think?"

That's a very good question Bart - I'm a string quartet player, and this is the solution that we have.

If the B happens briefly, as a passing/melodic note, then we play it slightly higher. However, if it is clearly played as part of chord 5, then we play it as a natural interval. Maybe you've experimented and come to the same conclusion as me.

October 12, 2008 at 05:44 PM · Neil,

My "solution" is along the same line as yours, but not as professional. Whenever the leading tone sounds long and is in a harmonic setting enough for me to care about it, it's probably going to be low; and I suspect that I play the others high very often.

Bart

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