REVIEW We have previously learned that a musical interval is the difference between two frequencies. This difference is expressed in terms of the numerical count from one pitch to, another together with a qual- itative designation which enables describing the difference between two intervals which have the same count. Thus the interval from C3 to G3 is a Perfect 5th. The interval C3 to E3 is a Major 3rd. And the interval C3 to Eb3 is a Minor Third. Each of these intervals is one which we have discussed. We will now learn about others. INTERVALS IN THE MAJOR SCALE One approach to learning intervals is to think of them in relation to a known pattern. The major scale is one such pattern. Its famil- iarity makes it useful for learning intervals. Because scale degrees are numbered, 1 through 8, the numerical designation of an interval from "prime" (or "unison") to "octave" is immediately at hand. In relation to the key note, any other scale degree may be labelled according to its position in the scale. The second scale degree is an interval of a 2nd in relation to 1; the 3rd scale degree is a 3rd, and so on. In the major scale pattern these intervals have the following qualitative designations: EXERCISE 1 "H" = to hear key tone "I" = to hear note within key (no larger than P8) "R" = ready to identify "N" = next "Alt/F" = to save score to disk "+,-" = to advance or reverse pages Listen to key tone. Listen to 2nd pitch. Identify with number and quality. M for Major (M2,M3,M6,M7). P for Perfect (P1,P4,P5,P8). INTERVAL TRANSFORMATIONS Once the quality of a given interval is known, altering the actual number of half-steps contained in the interval while retaining the numerical designation transforms the quality. We have previously learned, for instance, that a Major 3rd made smaller by a half step (lowering the upper note, or raising the lower note) becomes Minor. The intervals just learned are either Major or Perfect. Here are the "rules of transformation" involving these intervals: -Major intervals made larger by a half-step become Augmented -Major intervals made smaller by a half-step become Minor -Perfect intervals made larger by a half-step become Augmented -Perfect intervals made smaller by a half-step become Diminished -Minor intervals made smaller by a half-step become Diminished -Diminished intervals made smaller by a half-step become Doubly- Diminsihed -Augmented intervals made larger by a half-step become Doubly- Augmented I like to put these formulas into a simple code, in which ">" (greater than) means "made larger" and "<" (less then) means "made smaller." M > 1/2 = A M < 1/2 = m P > 1/2 = A P < 1/2 = d m < 1/2 = d d < 1/2 = dd A > 1/2 = AA Examining each of the intervals of the major scale with their half- step transformations leads to the following qualitative changes: This procedure reveals a difficulty we've encountered before: enharmonic equivalents. The interval of an augmented second sounds the same as a minor third. How is one to know when to use which, or, if identifying intervals aurally, which is which? As with most everything else within the realm of an art which is based upon the manipulation of patterns, the answer is CONTEXT. Understanding a given context requires knowledge of all the partic- ulars constituting that context. This is often a life-long pursuit. We can, fortunately, learn enough about the particulars early on to at least begin understanding the larger context and thus make decisions about specific usages, e.g. when an interval should be an augmented 2nd versus a minor 3rd. We have, in fact, seen this specific choice previously. Let's look at it again as an illustration. The largest context here is TONALITY. Within the system of tonality there exists a pattern of pitches known as MINOR. There are three essential configurations of minor. To maintain the integrity of the pattern, the interval between the 1st and 3rd scale degrees in each of the three configurations is minor. In one of the configurations, namely HARMONIC MINOR, the 7th scale degree is raised from its "natural" pitch according to the key signature. This results in the interval of an augmented 2nd from the 6th to the 7th scale degrees. In the context of tonality and within the context of the minor scale, these two intervals are readily distinguished both in spelling and in sound. The minor 3rd sounds like a minor 3rd; the augmented 2nds sounds like an augmented 2nd, even though if heard in isolation each would sound identical to the other. INTERVALS BY HALF-STEPS The more ways we have of approaching a subject the more prospect there may be for understanding it. Another way of learning inter- vals is to count half-steps. Taking the intervals examined through the process of transformation above, we can construct a chart: Half-Steps: 0 1 2 3 4 5 6 7 8 9 10 11 12 Interval: P1 m2 M2 m3 M3 P4 A4 P5 m6 M6 m7 M7 P8 A1 A2 d5 d7 The top row of intervals are the most common. The second row are likely enharmonic equivalents. Other possibilities, like d2 as an enharmonic equivalent for P1 are rare. We have also exluded from this chart any spellings involving doubly-diminished or doubly- augmented intervals, which are also uncommon. You should under- stand how these may be derived, however. INTERVALS IN THE MINOR SCALE Another means of identifying intervals is to see and hear them in the context of the minor scale. The intervals which are different here from the major scale pattern are the minor 3rd, the minor 6th, and the minor 7th. EXERCISE 2 "H" = to hear key tone "I" = to hear note within key (no larger than P8) "R" = ready to identify "N" = next "Alt/F" = to save score to disk "+,-" = to advance or reverse pages Listen to key tone. Listen to 2nd pitch. Identify with number and quality. M for Major (M2). P for Perfect (P1,P4,P5,P8). m for minor (m3,m6,m7). IDENTIFYING INTERVALS BY EAR We have already had some practice in identifying intervals by ear, in the context of either the major or minor scale. Another way to hear isolated intervals is in association with the interval with which a familiar tune begins. Here are some examples: INTERVAL IDENTIFICATION "H" = hear interval "S" = see 2nd note "R" = ready to identify At 1st prompt, enter QUALITY (P,M,m,d,A) and NUMERAL (e.g. P5). At 2nd prompt enter 2nd pitch (use bb for Double Flat, ## for Double Sharp) ("H" to hear again "S" to see 2nd pitch on staff or to see name of note) "N" = next Alt/F = save score F =return to menu