This course assumes that you have a basic knowledge of how to raise and lower pitches in standard music notation. If you need to review proper usage of accidentals, please refer to the Further Reading section under Discussion 1b.
When studying tonal harmony, C-sharp and D-flat have unique functions and are not interchangeable, however, when considering their acoustic properties, there is no difference between these two pitches. At its core, enharmonic equivalence is an easy concept: When two pitches sound the same – meaning that they share identical wavelength frequencies – but have different note names (i.e. letters), we consider them to be enharmonically equivalent. All pitches that are enharmonic equivalents create a pitch class, meaning that there are twelve pitch classes in traditional Western tonality. Every pitch has multiple enharmonic equivalents, but some are used less frequently due to the necessity for uncommon accidentals such as double-sharps and double-flats. Note that all but one pitch class has at least three enharmonic equivalents when using the five most common accidentals: naturals, flats, sharps, double-flats, and double-sharps. (The remaining pitch class only has two possible enharmonic equivalents without creating accidentals that exist only in theory such as triple-sharps or triple-flats.)
Using the example below, determine:
Using the example above, you can extrapolate which pitch classes have three enharmonic equivalents and which have two. The first two examples given were:
A, B-double-flat, G-double-sharp B, C-flat, D-double-sharp
Each pitch in these groups belong to the same pitch class, because they share an identical frequency in their sound waves. Yet they function differently within the context of music, so we have multiple ways of labeling the same frequency.
The most important realization was that letter system employed in staff notation is the limiting factor in creating enharmonic equivalents within a pitch class. The pitch class that includes A-flat is isolated from its neighbors in such a way that there is no pitch that uses the letter F or B to create a third enharmonic equivalent if we limit ourselves to only the five common accidentals. The interaction between the 7 letter names and 12 pitch classes is the basis for our musical notation system and will be critical in how we label intervals, chords, and scales.
When labeling pitches, we also need a way to refer to specific octaves or registers. We will be using the system used by the International Standard Organization (ISO). In this system, each pitch is given a numeral that designates its octave. For example, middle C is labeled as C4.
Using the example below, determine:
There are a few simple rules to label octaves using the ISO system.
You were given that that C4 is middle C, and from this, you should be able to determine where middle C is on each clef
From this, it is easy to see the necessity of clefs. Ledger lines are an important notation tool, but too many ledger lines becomes difficult to read quickly. Therefore, each clef highlights a specific range that can be written without employing ledger lines. Alto clef is typically thought of as a lower extension for treble clef; it adds the visual space of seven steps from treble clef. Tenor clef is a higher extension for bass clef and adds the visual space of five steps from bass clef. Of course, alto and tenor clef have similar ranges and one of the other could likely be eliminated with little issue – alto clef is visually seven steps from either treble or bass clef – but because both of these clefs have been widely used for more than a century, it is necessary for all musicians to be familiar with reading them.
This is almost entirely related to the evolution of the musical notation system and how the non-accidental pitches (i.e. “white keys” of the keyboard) form a major scale. While this is a fascinating topic, it is somewhat beyond the purview of this chapter, but I hope you will explore this further on your own.