Temperaments (equal or otherwise)
On the music theory book thread someone talks of the obscurity of books on temperaments. But being new to string instruments, I am curious.
On a piano ET is achieved by the fifths being a little flat and the thirds a little sharp, yet string instruments tune in perfect (3/2) fifths. That immediately puts you out of tune with a piano accompaniment, doesn't it, unless you tune your 4 strings to the piano's notes? And then those perfect fifths make it tricky to intonate the different scales that employ those open strings. Someone asked about warming up a while back, and at the moment, I find my warming up consists of simple scales finding the correct ET intonation on those JI strings. It probably becomes second nature. Or is it possible that you have to give it thought now and then?
I'm sure we've had thread on this before!
True, equal temperament does not fall "naturally" on the ear. And it may be best to tune your A and G strings to the piano you play music with - especially if the music you will play together includes an open G string, although the difference between Gs tuned in equal and just temperaments is still quite small and undetectable by most people. For violists and cellists directly matching their lowest (C) strings to the piano is important. According to their former cellist, David Finckel, the Emerson String Quartet tuned their instruments to tuners rather than in "perfect" fifths. It avoided any related arguments.
Chris, like all forums, most threads will be repeated often. I was criticised a few months back for bumping a two-week-old thread and told I should have started another, lol!
The Bach Partita example that Chris mentioned is here:
The answer to the apparent conflict between the piano and most other instruments is.....
Temperaments are for accommodating the inflexibility of fixed pitch instruments (keyboards and frets, mostly). All other instruments have the ability to adjust the pitch according to context, and temperament is an irrelevant concept for them. The pitch of every note in a flexible system depends only on the context, the intent, the movement that's intended to be expressed, not a rule.
Adrian, you're indulging in terms and concepts that most people on this forum won't understand.
Scott, of course we don't think "Pythogorean" etc. while we play, but these terms occur in discussions and documents, and I was trying to offer true, but brief, descriptions. If we are attentive to minute shifts in pitch while practicing alone, we will be better able to navigate our kayak in the presence of others!
The topic comes up frequently. The limit of pitch discernment for the trained musician is reported to be 5-6 cents. A cellist or violist that tunes to the piano A does not notice the pitch difference on the other strings until the C-string, 6 cents different, and might tune the C up a little, depending on the key. My approach to it is that there are three systems of intonation in modern western music: Equal-tempered, piano style tuning, which is good enough most of time. Horizontal/ Melodic/Pythagorian tuning, and Vertical/Chordal/Just intonation. In practice, each note is a cluster of three spots, +/- 10 cents, only 1 mm apart or less (!), high-neutral-low. You tune to the context. Just being aware of it helps. As long as you don't bend a note in the wrong direction you are OK. And - a good vibrato is wider than that. Vibrato covers a multitude of sins.
Adrian's summary on this really difficult subject of temperaments is really succinct and nicely done I think!
I'm getting tendinitis in my right index finger from scrolling posts like that on my old screen!
For those with a great interest in the development of equal temperament, I highly recommend the book Temperament by Stuart Isaacoff: https://www.amazon.com/Temperament-Became-Battleground-Western-Civilization/dp/0375703306/ref=sr_1_1?s=books&ie=UTF8&qid=1548001874&sr=1-1&keywords=temperament+isacoff. One thing that fascinated me is that many great thinkers during the relevant period got involved in the issue, including people like Sir Isaac Newton.
"Great point about relative "perfect pitch" being more essential to quality musicianship than whatever else one might be able to muster up."
In that long post David M. mentioned "leading tones" My opinion is that that concept should be left in the functional harmony books and Not applied to intonation. "Leading tone intonation" aka "expressive intonation" sometimes, definitely not always, causes pitches that do not fit well into the chords; 1/2 steps too close, minor thirds too narrow, major thirds too wide. Violists and second violins in good string quartets learn to bend the notes a little in different directions. I have had some success in teaching lower level students how to play the chromatic scale (there is only one!) better in tune; alternate big and small half-steps; half-steps on the same finger wide, half-steps on adjacent fingers tight. This is partly an illusion, it compensates for the natural tendency to play out of tune. When to use neutral, tempered intonation ? : when playing with a piano, non-tonal musics, the fast chromatic scale, whole-tone scale, the two ambiguous, symetrical chords: diminished chord, augmented chord.
continued-- by "natural tendency to play out of tune" I meant physical, anatomic. If you ask a day one beginner to place four fingers on the fingerboard where they are most comfortable, those notes will be out of tune. We practice our scales, arpeggios, double-stops, to train our fingers to correctly measure the distance between the notes, the interval distances. --- Theory is not fantasy, but should be a logical, mathematical, model of what we observe in nature. The frequency of air pressure differences is real, while sound is how our brain interprets them. The analogy with light is : color is how our brain interprets small differences in wave-length.
I like to tune a bit sharper than the piano in most cases. Makes the violin brighter.
Sometimes I get the impression that if only one can work out the difference between ET and JI, then we are 99% there : )
Practical example (from a workshop on a C major quartet):
"ometimes I get the impression that if only one can work out the difference between ET and JI, then we are 99% there : )"
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