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• Ear Training
• Understanding Notation
• Relative Pitch - The recognition of Melodic Intervals (Distance Ascending or Descending) and Harmonic Intervals (Consonant or Dissonant Quality); recognition of Chords by Function (Tonic, Dominant, or Subdomiant/"Predominant")
• Absolute Pitch - The recognition of specific Notes and Chords by name (i.e.: distinguishing the "density" or number of Notes and their particular frequencies; similar to recognizing distinct Hues and Color Mixtures in sight)
• Rhythmic (Time) Feel - Feeling the regular pulse of a piece of music and being able to count steadily to it
How are the above aspects notated? In general, the X-axis of the staff is Time and the Y-axis is Pitch. However, there are more specific details as well. For example, in regards to Rhythmic (Time) Feel:
• The relative duration of individual sounds and silences are given by types of Notes and Rests (i.e.: Whole, Half, Quarter, etc.).
• Time Signatures give the Note/Rest length which is used as a Beat (i.e.: the regular pulse), and how to group those pulses into repetitive cycles (Measures/Bars) by Counting.
• The number of Beats Per Minute is the Tempo (i.e.: the overall speed of the piece of music).
There are also symbols which give insight into other aspects:
There are "Articulation" markings which tell how to shape the envelope of the sound (e.g.: "Legato" is to smoothly connect a sequence of Notes together through an even attack, while "Staccato" is to keep them distinct from one another through a sharp attack).
There are "Dynamic" markings which show the volume of a sound (e.g.: "Piano" means to play quietly through a soft touch, and "Forte" means to play loudly by using more force), and how to vary that volume (e.g.: "Crecendo" is to get progressively louder, while "Diminuendo" is to get progressively quieter).
There are markings which tell one to...
• Hold (e.g.: "Fermata")
• Repeat (e.g.: "Double Barlines w/ 2 Dots", "Multiple Endings and Variations w/ Numbered Sections", "Coda Signs w/ DC and DS", "Measure Repeat Sign")
• Add or Vary Something (e.g.: "Grace Notes", "Ornaments", "Glissandos", etc.)
How do you play what you hear and read in a way that is ergonomic (i.e.: healthy and efficient)? How familar are you with navigating your instrument; is it so familar that it has become an extension of you?
In general, there is a unity between ears (Ear Training), eyes (Understanding Notation), and hands (Technique).
• Sight-Reading - Playing directly from notation without study
• Playing By Ear - Mimicking what is heard on an instrument
• Transcription - Notating what is heard
• Arrangement - Changing a pre-existing piece of music (whether it be by reinterpreting the content or using different instruments to play it than the original)
• Composition - Writing new music
• Improvisation - Making new music on the fly, usually in a live setting with other musicians (sometimes called "Jamming")
Notice that all of these skills require a deep familarity with the previously mentioned skills (i.e.: Ear Training, Understanding Notation, and Technique).