POSTLUDE: Fundamentals of Music (Review – From “Open Music Theory”)
24 American Standard Pitch Notation (ASPN)
Chelsey Hamm and Bryn Hughes
Key Takeaways
- American Standard Pitch Notation (ASPN) provides labels for specific musical frequencies by combining a note name (such as C) with a subscript octave designation (such as 4).
- A pitch is a discrete tone with an individual frequency (e.g. C4), while a pitch class is less specific (e.g., C in general).
- ASPN differentiates between octaves, from C to B. The octaves are labeled from lowest to highest, beginning with 0 and continuing in ascending numerical order (1, 2, etc.).
- A piano keyboard primarily uses the ASPN octave designations 1 through 7, although small portions of octaves 0 and 8 are included.
- Middle C is C4 in ASPN. It is helpful to memorize the ASPN label of this note as a starting point.
American Standard Pitch Notation and Pitch versus Pitch Class
In order to discuss specific notes, or pitches, we will use American Standard Pitch Notation, abbreviated ASPN. ASPN designates specific musical pitches by combining a note name (such as C) with a subscript octave designation (such as 4), creating a bipartite label (for example, C4). ASPN labels are very useful, since they can identify every possible musical note within human hearing range, from the lowest pitches to the highest.
The Reading Clefs chapter introduced octave equivalence, the concept that explains why notes one or more octaves apart have the same letter name. Music theorists distinguish between a pitch, a discrete tone with an individual frequency (e.g. C4 using ASPN), versus a pitch class, which is less specific (e.g., C in general). A pitch class includes all the pitches with the same letter name, in any octave, along with their enharmonic equivalents. For example, all Cs are the same pitch class, and the enharmonically equivalent notes D𝄫 and B♯ are also part of the C pitch class. In this chapter we are naming specific pitches with ASPN.
ASPN and Octave Designations
ASPN differentiates between octaves, beginning with the pitch C and ending with the pitch B. This means that each new octave designation begins on the note C, as seen in Example 1. The octaves are labeled from lowest to highest, beginning with 0 and continuing in numerical order (1, 2, 3, etc.). The pitch middle C is C4, which is useful to memorize.
All letter names within an octave (below the C of the next octave) receive the same octave designation. For example, all of the notes in Example 2 would be designated in the 4 octave, because they are above C4 but below C5. Accidentals applied to a note do not have an effect on its ASPN number. For example, B♯3 and C4 have different octave numbers despite being enharmonically equivalent, because the B♯ is still considered part of the lower octave.
ASPN and the Keyboard
ASPN labels are very helpful for finding specific notes on the piano keyboard. Example 3 depicts a piano keyboard with each octave labeled using ASPN notation. As you can see, the piano keyboard spans the full octaves 1 to 7. It also contains a small part of both octaves 0 and 8. ASPN labels are the same regardless of instrument or voice type. In other words, a C4 will always be labeled as such regardless of whether it is produced with a flute, trombone, violin, or voice.
ASPN and Staff Notation
Example 4 shows ASPN labels for common notes in the treble, bass, alto, and tenor clefs. Memorizing the location of C4 in each clef can make finding ASPN labels quicker and easier.
https://musescore.com/user/32728834/scores/8395191/s/5sFqPN/embed
Example 4. ASPN labels for notes in four clefs.
- “Pitches, Pitch Classes, Octave Designation, Enharmonic Equivalence” (YouTube)
- Tutorial on ASPN Octave Labels (liveabout.com)
- Tutorial on ASPN Octave Labels (flutopedia.com)
- Helpful Graphic with ASPN Labels on the Grand Staff and Piano (Music Theory Tips)
- Flash Cards with ASPN Labels in Treble and Bass Clefs (quizlet.com)
Key Points
In this chapter we learn about the minor mode, how it evolved in tonal music and how we might best use it.
We will cover the following:
- Seventh Chords in the Major Mode
- Preparation and Resolution of the Dissonance and the Chord Progression Schema for Seventh Chords
- Inversions of the Seventh Chord
- Connecting Seventh Chords to One Another
Until now, our study of tonal music has focused on materials and techniques using only one of the seven diatonic modes: the major mode. However, in tonal music, we also have another mode available to us: the minor mode. The modern, tonal minor mode slowly evolved through compositional and performance practices, using the Aeolian mode as a foundation, borrowing elements from the other two minor-like diatonic modes of Dorian and Phrygian. One might reasonably ask why it was necessary to wait until now to begin our study of the minor mode but, as you will see, because it shares characteristics of all the diatonic minor-like modes, it contains peculiar features and characteristics which need more care and attention in practice to use and understand the mode effectively, and to obtain the unique sound and flavor of minor to which it offers.
The Three "Flavors" of Tonal Minor
As mentioned above, the modern, tonal minor mode evolved through compositional and performance practice over several centuries in Western music to incorporate aspects of each of the diatonic minor-like modes. As you may recall from your fundamentals study, there are three possible configurations of the tonal minor mode: Natural, Harmonic, and Melodic. These three terms refer to the ways in which each variation is deployed within a musical setting. First, let us first quickly review each one.
Natural Minor (Aeolian)
So-called "natural" minor is simply the unaltered version of the diatonic Aeolian mode.
Figure 1. Natural Minor, in scale order, built on pitch class A.
Harmonic Minor
The first variation of natural minor is known as "Harmonic" minor. It is the natural minor mode with a raised seventh scale degree.
Figure 2. Harmonic Minor, in scale order, built on pitch class A.
As you likely learned in your study of music fundamentals, the natural minor mode does not contain a leading tone but rather a subtonic with [latex](\hat7)[/latex] a whole step below the tonic. This is one of a few important differences between the major mode and the minor mode. In Harmonic minor, the [latex](\hat7)[/latex] is raised by a half-step, creating an artificial leading tone which then gives us the ability to have a strong tonal harmonic progression in cadences, similarly to how the major mode behaves intrinsically (as we will learn more about shortly). It this use of the artificially created leading tone in harmonic progressions that give this variation its name ("harmonic").
Melodic Minor
The second variation of natural minor is known as "Melodic" minor. It is the natural minor mode with a raised seventh scale degree, just as we have in Harmonic minor, but also contains a raised sixth scale degree.
Figure 3. Melodic Minor, in scale order, built on pitch class A.
Like Harmonic minor shown above, Melodic minor also contains an artificial leading tone by way of a raised [latex](\hat7)[/latex] for the purpose of strong tonal cadential progressions. However, unlike Harmonic minor, the Melodic minor variation adds a raised [latex](\hat6)[/latex] which now smooths out the awkward interval of an augmented second (A2) between [latex]\uparrow\hat6[/latex] and [latex]\uparrow\hat7[/latex] that we find in Harmonic minor[1]. Now, instead of the augmented second between 6 and 7, we have a smoother melodic interval of a whole step. Hence, the name "melodic" simply refers to this smoothing out of the augmented second we find in Harmonic minor.
The Major-Major Seventh
The Preparation and Resolution of the Dissonance
The dissonance, the harmonic seventh as a chord tone that sounds against the root, is handled in the same way as the diminished fifth chord tone in the diminished triad. We must first choose a chord that contains the pitch class that will become the dissonant seventh chord tone in the chord preceding. Then, after sounding the seventh chord in question, we resolve the dissonance by moving the voice containing the seventh chord tone downward by step into a chord that contains the resolving pitch as a consonant chord tone. In the case of the half-diminished seventh chord, where we have two dissonances (the seventh and the diminished fifth chord tones in relation to the root), we need to doubly prepare and doubly resolve each dissonance. Later these strict guidelines will be relaxed as our ability to enrich our harmonic phrases will increase.
Unlike the diminished triad which occurs on only the leading tone, we have the opportunity to build and use seventh chords on all seven scale degrees of the major mode. Thus, to accomplish the successful handling of the dissonant seventh, we need to locate appropriate preparation chords and resolution chords which will work with any of the available seventh chords. The chart below summarizes each of the different possible preparation and resolution schemes for each of the seventh chords we have available to us in the major mode. Later we shall adapt and modify this chart for the minor mode.
Seventh Chord Preparation and Resolution Schema
PREPARATION |
SEVENTH CHORD |
RESOLUTION |
|---|---|---|
Dominant (V) Mediant (iii) |
Tonic (I7) |
SubDominant (IV) |
SubMediant (vi) SubDominant (IV) |
SuperTonic (ii7) |
Dominant (V) |
Leading-Tone (vii) Dominant (V) |
Mediant (iii7) |
SubMediant (vi) |
Tonic (I) SubMediant (vi) |
SubDominant (IV7) |
Leading-Tone (vii) |
SuperTonic (ii) Leading-Tone (vii) |
Dominant (V7) |
Tonic (I) |
Mediant (iii) Tonic (I) |
SubMediant (vi7) |
SuperTonic (ii) |
SubDominant (IV) SuperTonic (ii) |
Leading-Tone (vii7) |
Mediant (iii) |
Summary
We may summarize what we learned above in three step process as follows:
- Prepare the dissonant seventh chord tone by sounding it first in a preceding chord as a consonant tone and then tying it over as a common tone. For the leading tone half diminished seventh, we need to prepare both the seventh and the diminished fifth dissonances. Use the chart above to refer to chords that could be used to prepare a seventh on any given scale degree in the major mode.
- Sound the seventh chord by holding over the dissonance(s) and any other common tones, then moving the other voices to the next nearest chord tones to complete the chord. As we are sounding a seventh chord, no doubling is necessary. However, we do need to make sure we have a complete chord. For now, do not omit any chord tones (later we will be able to relax this condition).
- Resolve the dissonance(s) by moving to the resolution chord and moving the voice containing the dissonant seventh chord tone (or both the seventh and the diminished fifth) downward by step, holding over any tones in common, and moving the other voices to the nearest available chord tones. Again, mindful of trying to double the root when possible when moving to a triad.
- When resolving to a triad, move to the resolution chord found in the chart which is, for now, always found a root motion of a fourth upward from the scale degree on which we sounded the seventh chord. The concept of relative root motions of chords in harmonic progressions is a very important one and will become more and more important as we move further in our study.
- It is possible, and sometimes desirable, to connect sevenths to one another. There are no special additional guidelines for this so long as you are able to properly prepare and resolve the dissonance(s) and also satisfy quality voice leading with all of the guidelines we've covered and discussed thus far.
Chord Connection Guidelines: V4
Now that we have added seventh chords to the mix, we can add and adjust our tonal harmony progression flowchart:
Common Tone Chord Chart (Major Mode)
| Chord | Has common tones with... | |||
|---|---|---|---|---|
| I | iii | IV | V | vi |
| ii | IV | V | vi | vii |
| iii | I | V | vi | vii |
| IV | I | ii | vi | vii |
| V | I | ii | iii | vii |
| vi | I | ii | iii | IV |
| vii | ii | iii | IV | V |
Seventh Chord Preparation and Resolution Schema
PREPARATION |
SEVENTH CHORD |
RESOLUTION |
|---|---|---|
Dominant (V) Mediant (iii) |
Tonic (I7) |
SubDominant (IV) |
SubMediant (vi) SubDominant (IV) |
SuperTonic (ii7) |
Dominant (V) |
Leading-Tone (vii) Dominant (V) |
Mediant (iii7) |
SubMediant (vi) |
Tonic (I) SubMediant (vi) |
SubDominant (IV7) |
Leading-Tone (vii) |
SuperTonic (ii) Leading-Tone (vii) |
Dominant (V7) |
Tonic (I) |
Mediant (iii) Tonic (I) |
SubMediant (vi7) |
SuperTonic (ii) |
SubDominant (IV) SuperTonic (ii) |
Leading-Tone (vii7) |
Mediant (iii) |
EXAMPLES: Seventh Chords in the Major Mode
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RWU EXERCISES
Mixed Triads and Seventh Chords in Short Phrases
Using the templates below, do the following:
A) ROOT POSITION SEVENTH CHORDS
- Realize the given harmonic progression (the Roman numeral analysis is provided). You may choose inversions of the triads as you wish within the guidelines.
- Compose three harmonic progressions of your choice, at least 8 to 12 chords in length, one may be in C Major, and the other two any major key of your choosing.
- Follow the guidelines set above.
- You must have at least two seventh chords per phrase, but not more than three. Try, across your three attempts, to use one of each possible seventh chord found on each of the seven scale degrees.
- You must have at least one instance of a leading tone diminished triad OR half-diminished seventh chord in each of your phrases, properly prepared and resolved according to the guidelines above.
- Use triad inversions wherever you wish according to the already established guidelines for voice leading. Strive for a decent mixture of root, first, and second inversion triads to complement the seventh chords.
B) INVERSIONS OF SEVENTH CHORDS
- Compose three harmonic progressions of your choice, at least 8 to 12 chords in length, one may be in C Major, and the other two any major key of your choosing. Follow the guidelines above except this time, when using the seventh chords, you may use inversions. Strive for a good mixture of different inversions and root position for both practice and variety. You may also try to connect seventh chords to one another--you should have at least two instances across your three phrases.
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Schoenberg Theory of Harmony Examples
Further Reading
- Schoenberg, Arnold: Theory of Harmony
- Schoenberg, Arnold: Structural Functions of Harmony
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In church modes, the final loosely corresponds to the modern notion of "tonic," in that it is a melodic goal. However, the final may not always be emphasized in the way a tonic is. Finals are named by the fact that the last note of a Gregorian chant will always be the final of the mode.
