INTONATION:

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INTONATION

• The control of overall pitch level and individual
  pitches in relation to other relevant pitches.

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Good Intonation is

• Properly controlling the pitch level of every
  note played, relative to the pitch level of any
  note(s) played immediately before, and any
  note(s) played simultaneously.

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Group Tuning Before Making Music

• The purpose of having everyone in the ensemble
  tune their instrument to the same reference pitch
  is to get roughly close to the same overall pitch
  level, so that fine tuning each note as you play
  will be easier to accomplish! This is merely a
  starting point for real tuning.

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When tuning your instrument in a group setting
you should

• 1) Remember that the temperature and humidity of
  the instrument, and the playing environment, as
  well as embouchure formation and conditioning,
  significantly affect overall pitch level.
  Therefore, you should always warm-up before
  tuning your instrument to a reference pitch.
• 2) When the reference pitch is sounded, do not
  begin playing immediately. Listen to the sound
  long enough to hear it in your mind.

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• 3) When tuning your instrument, DO NOT adjust the
  pitch by changing your embouchure, hand/finger
  position, etc. These are means of fine tuning
  individual notes. The purpose of group tuning is
  to get the overall pitch level as close as
  possible to the others with whom you will be
  playing.
• 4) Make all adjustment to your instruments
  overall pitch level by changing the length of the
  sounding chamber, or the tension of the vibrating
  object. (Remember the principle Longer Lower
  Shorter Higher) Also, be aware of how much
  instrument length change is required to
  significantly affect pitch.

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• 5) Ideally, group tuning should be done on a
  pitch that is a known to be a good note for every
  instrument. However, there is no single pitch
  that is a good choice for every instrument.
  Therefore, a group should tune to several
  different pitches, focusing on the instruments
  for which each pitch is a good note, when that
  note is sounded. (A good note would be one that
  is easily played with a good clear tone, and is
  close to the center of the overall pitch level of
  the instrument being tuned.)

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• 6) Be certain you are using a correctly formed
  embouchure, when checking the tuning of your
  instrument. Avoid playing notes at the extremes
  of your pitch range, unless you have fine control
  over those notes.
• 7) Be certain to maintain a steady volume and
  flow of air when tuning your instrument.

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• 8) Take care not to move your jaw, tongue,
  fingers/hand, or anything else that can affect
  the pitch, or volume of your instrument, while
  you are tuning your instrument to the reference
  pitch.
• 9) Once your instrument is tuned as closely as
  possible to the overall pitch level of the group,
  THEN you can work on adjusting (fine tuning) the
  pitch level of every note you play.

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Fine Tuning

• Note If you as a player can not independently
  adjust each of the tone controlling variables,
  you will not have control of your level of pitch.
  (See presentation on TONE for an explanation of
  tone controlling variables.)
• Fine tuning is accomplished by making small
  adjustments to your embouchure, finger position,
  hand position, jaw position, air flow etc.

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The Two Planes of Pitch Fine Tuning

• Horizontal Melodic
• Vertical Harmonic
• As a member of an ensemble you must be aware at
  all time of the nature of your part.
• You must know if it is melodic or harmonic, and
  tune accordingly.

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Horizontal or Melodic Tuning

• When you are playing a melodic musical idea you
  must hear it in your mind and be certain that
  each interval of pitch change is correct. When a
  stream of pitches moves up and down, each move
  should be an exact distance (Interval)

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Vertical or Harmonic Tuning

• When you are playing a note that is a part of a
  chord or other multi-pitch sonority, you must
  fine tune your pitch level for each note played
  based on its relative highness or lowness as
  compared to the other pitches in the sonority at
  that instant.
• Harmonic tuning is best accomplished by correctly
  spacing the various pitch intervals in a
  multi-pitch sonority using (just intonation)

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JUST INTONATION

• Just intonation is based on the Harmonic Series
  as defined by Pythagoras. His theory of sound
  states that there is a natural mathematical ratio
  for every interval. These intervals are not
  exactly the same as equal temperament tuning
  gives us. Therefore, pitches must be adjusted in
  order to make the interval sound correct. It is
  the distance between the various pitches that
  matters, not the exact highness, or lowness as
  indicated by a chromatic (equal tempered) tuner.

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Pythagorean Illustration of Harmonics
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The Harmonic (Overtone) series with indications
of the natural deviation in cents from equal
temperament tuning.
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The sum of an interval and its inversion is 9,
except for an octave
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Pitch Interval Adjustment Table(Changing Equal
Temperament to Just Intonation)
Pitch Interval Interval Distance Adjustment in Cents (1 cent 1/1200 of a 8va) 50cents is up a ½ step 50 cents is down a ½ step
Perfect 5th 2 cents
Perfect 4th - 2 cents
Major 3rd -14 cents
minor 6th 14 cents
minor 3rd 16 cents
Major 6th -16 cents
Major 2nd 4 cents
minor 7th - 4 cents
minor 2nd 12 cents
Major 7th 12 cents
Augmented 4th -10 cents
diminished 5th 10 cents
Perfect Octave No adjustment














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Ideas to remember

• Most tuning problems in a group are actually
  misplayed/wrong pitches.
• Good Intonation is about interval distances, not
  an exact frequency of vibrations/second.
  Therefore, if two people are playing an interval,
  and both adjust their pitch in order to make the
  intervallic distance correct. It does not
  require the player with the upper pitch to adjust
  as much. (In other words they should compromise
  on pitch level to make the interval sound
  correct.)
• Tuning with equal tempered instruments, such as
  keyboard instruments, and keyboard percussion,
  can be difficult at times.

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NOW TUNE IT OR DIE!!!