Note: This is a work in progress. It is not complete. I've probably said something that doesn't make sense, or I rambled, or I'm just plain wrong somewhere. This started as a "stream of thought" piece, so it will take some fleshing out to make it completely coherent.
I believe that the art of music making can be broken down into small but manageable pieces that are related in a tree hierarchy. Thus I have attempted to organize my thoughts in this manner.
Everything in this tree is in order of importance.
Technical
Music making is a largely technical pursuit. This may be an unpopular opinion, but I defy someone to play a violin concerto on pure artistic fortitude. However, we do find ourselves listening to performances at the highest technical skill level, but lacking an artistic quality. It does work, in spite of being less than interesting. It is partly for this reason that this section dwarfs the "Artistic" section. This is also due in large part to the fact that technique can be quantified, whereas art cannot.
Individual
This section identifies aspects of technique that are specific to individual practice. These fundamentals can only be addressed on an individual level, and are prerequisite to developing ensemble skills.
Musical
This includes all of the fundamental principles of music. It is best to remove the technical complexities of the instrument whenever possible in order to work on these things.
Time
Time is the foundation of music. Music, simply put, is sound over time. The type or quality of the sound is secondary. The utmost emphasis should be placed on time.
Pulse
Most music is metered. Therefore, you must have a very stable way to measure the time. The way to do this is to endeavor to internalize a stable pulse. You need to be able to do this at a variety of rates (i.e. tempi). And you need to be able to vary that tempo in a smooth, linear fashion in order to affect gradual changes in tempo. Furthermore, you must be able to subdivide the base pulse into smaller units for accurate placement of rhythm.
Rhythm
Rhythm, quite generally, is the process of choosing pulses onto which events must occur. It is best to simplify at first by concerning one's self only with one type of event. A clap is an excellent instrument for this purpose, as there is only one event: the clap itself. Then choose an instrument that has duration, such as a recorder. Now you have two events: start and end. The start event is considerably more important than the end, as the end is often dictated by style rather than by the written rhythm. Rhythm should be taught in tandem with reading, and emphasis should be put on the start event, not duration. See the section on reading for more.
Pitch
Intonation of intervals
Start with the most consonant intervals and work your way toward dissonance. The development of the ear starts with hearing intervals played simultaneously. Then you can work on hearing the intonation having them played in succession. You should be able to tell whether the interval is too small or too large, and thus deduce how to adjust. The exception is the unison; since the goal is to produce the same pitch, it is often difficult to know whose pitch is above and whose is below. While the unision is easiest to hear when in tune, it is the most difficult to determine how to correct when it is not.
A possible ranking of intervals from most consonant to most dissonant is:
P1, P8, P5, P4, M3, m6, m3, M6, M2, m7, m2, M7, d5
Intonation of chords
This is the natural progression from intervals. Assuming that you are in charge of just one pitch in the chord, and all the other pitches are in tune with each other, then it should be quite easy to place. Initially hearing whether the pitch is sharp or flat can be harder because of the extra "interference", but once you are used to it, it will actually make it easier. It should be noted that it isn't technically possible to tune a note in a chord where the other notes are not also in tune. This is not within the scope of this section, but will be addressed in the "ensemble" section.
Reading
Reading and rhythm should be taught in tandem. See the section on time for more information. Once rhythmic concepts are mastered, then add reading of pitches. Rhythms should not be read as a series of durations. They should be read as a series of events in a metered time. The "note value" is just a way of letting you know where the next note comes in time. A note tells you when to play the next note. How long you choose to hold out a note is a matter of style. Four quarter notes in 4/4 time can be completely legato or very staccato, but their "start events" are still metered on the beats "1 2 3 4". The duration of the played pitch may very short, but the period between the beginnings of each note is unrelated to that duration. This is why it is best to avoid thinking of the written note as a duration. A firm understanding of this concept will help to prevent the dreaded rushing of short notes and dragging of long notes, and will improve reading ability in general. Sight-reading is critical to the practical musician and should be practiced daily. Endeavor to perform a piece that you have never seen as if you have always known it. This will also demonstrate your raw technical abilities on your instrument.
Instrumental
The following are fundamental things that are common among all instruments, including the voice.
Quality of sound
You should be able to make the instrument create its characteristic sound, and you should endeavor to do it consistently regardless of other technical difficulties. Certain instruments make this very easy (e.g. piano). Others make it much more difficult (e.g. violin). The instrument itself (i.e. the entire device, including mouthpiece, reed, bow, et al.) plays a significant role in this, and should not be overlooked. It is important that each performer find the correct balance between equipment and himself. The old saying about the poor musician who blames his instrument is not precise. It is a poor musician who always blames his instrument, but he who never considers that the instrument may be at fault is just as poor. The oboe is a great example of this. The quality of the reed is critical to a good sound, and as of the time of this writing, it is not possible to manufacture workable oboe reeds. Therefore reed making is possibly the most important aspect of an oboist's quality of sound. The trumpet is a great example of an instrument where the bulk of the responsibility rests on the player. In essence, the trumpet sound is created just as the oboe's sound is, except that instead of using a reed, one uses his own lips. Therefore this critical part of tone production is no longer an external component. It is interesting to note, however, that trumpeters tend more often to be consumed by matters of equipment than players of most other instruments. I believe this to be a phenomenon better explained through psychology, and is thus beyond the scope of this writing.
Accuracy
None of your hard-earned musical skills will show if you cannot manipulate your instrument accurately. The goal is to be able to demonstrate your accurate rhythm and impeccable pitch through your instrument. Be careful not to foresake the musical fundamentals. Incorporate these fundamentals into your instrumental technique.
Dexterity
Once you can manipulate the instrument well enough to produce sounds accurately, it is then time to attempt more complex musical constructs. This may include faster tempi, rapid rhythms, extreme ranges, large leaps, or anything else that may challenge your instrumental technique. Be careful not to lose accuracy as you extend your dexterity; these two things are very much interrelated. You cannot be truly dextrous if you cannot demonstrate it accurately.
Ensemble
Ensemble technique is all about listening and being flexible. The idea is to be able to pull off a singular musical effect with many individuals simultaneously. The only way to achieve this is to listen, be sensitive to what you hear, and be flexible enough to adjust accordingly.
Hierarchy
An ensemble is not effective without a clear hierarchy. This hierarchy is simple for small ensembles, and gets very complex for large ensembles. It is also important to understand that the "default" hierarchy is just a place to begin; the "effective" hierarchy is whatever the music demands. It takes ensemble experience to be able to determine this in real-time. TODO: Enumerate the hierarchies.
Time
The time lives in the music itself and nowhere else. You must internalize this time so as to be able to play with it. The conductor is not a metronome. He makes no sound (hopefully). It is technically impossible to play "with the stick" because you have to try to convert the stick, which is in the visual domain, to the time, which is in the aural domain. Different people have different reaction times, and thus will interpret the stick differently. Best of luck to you if you have one of those conductors who wants it like that; he is just going to get in the way of his goal. After all, the best ensemble technique is demonstrated by quartets and quintets, and they have no conductor at all. What is often called the "beat" of the baton is really called the "ictus". I prefer to avoid the term "beat" in the context of the baton; "beat" is usually considered synonymous with "pulse", and I want to emphasize that the pulse is in the music, not in the baton. Hence, I use the word "ictus" to refer specifically to the baton. This ictus gives the player permission to play; it is up to the player to determine where to place the time. The conductor will normally place his ictus slightly ahead of where he perceives the time to be. To increase the tempo, he will place the ictus further ahead. To decrease the tempo, he will place the ictus closer to his perceived time. But he must be careful never to place it behind the time; if he does so, he is conducting in the past, and he has no control. The conductor should never try to adjust the tempo simply by conducting faster or slower; this will cause the group and the conductor to tear apart from each other rather immediately. It is the ensemble's responsibility to react as a group to the whims of the conductor. The normal delay between the ictus and the beat gives the individual player the time necessary to "calibrate", if you will, his own delay between where he perceives the ictus and where the time in the ensemble exists.
Pitch
Balance
Style
Artistic
This is the other major component of music making. It is that rather intangible aspect that gives the performer the freedom (and perhaps responsibility) to go beyond the music on the page. Music making is not a purely mechanical process. There is subtle nuance in how the notes on the page are treated. And each performer has a different approach, sometimes subtle, sometimes overt. It is not possible to quantify the artistic qualities that a musician must posses. The best way to become more artistic is to listen critically to many performances, give many performances, and play next to great performers.