Whoa: Major and minor 4th and 5th

(At the time of this posting, JiMS inline interactive courseware brings up this page when students press the "Whoa!" button for more information on the naming of the qualities of the diatonic 4th and 5th.)

In the fundamental scales of Western music (pentatonic, diatonic, chromatic, etc.) each generic interval occurs in exactly two qualities, called specific intervals.

This property is generally called Myhill's property after John Myhill, who co-discovered it with John Clough and Gerald Myerson, as described here.

Many of Westen music's most salient features have been shown to arise from this property.

Hence, it is extremely important to expose, through musical nomenclature,
• The difference between diatonic intervals that have
- one width, and
- two widths.

• The similarity among diatonic intervals that have
- width, and
- two widths.

The English language's traditional interval-naming scheme fails on both counts. Instead of dividing the diatonic intervals into two kinds (one-width and two-width), naming the kinds consistently, and naming the two qualities of the two-width kind consistently, it divides the diatonic intervals into four categories:
• One-width: perfect unison and perfect octave
• Two-width, smaller perfect: the 4th (smaller perfect; wider augmented)
• Two-width, larger perfect: the 5th (smaller diminished; wider perfect)
• Two-width, major and minor: the 2nd, 3rd, 6th, and 7th (smaller minor; wider major)

Furthermore, the English language's traditional interval-naming scheme fails to make an important distinction between
• diatonic qualities, and
• chromatic alterations.

For example, it uses
• "diminished" to refer to both
- the narrower diatonic 5th and
- the chromatically-narrowed cersions of the other diatonic intervals.
• "augmented" to refer to both
- the wider diatonic 4th and
- the chromatically-widened versions of the other diatonic intervals.

In summary, the English language's traditional interval-naming scheme
• Fails to distinguish among entities that are different:
- By using the term "perfect" to describe both one-width qualities and two-width qualities
- By using the term "augmented" to describe both diatonic qualities and chromatic alterations
- By using the term "diminished" to describe both diatonic qualities and chromatic alterations
• Makes false distinctions among entities that are the same:
- By using the different terms "perfect," "minor," and "diminished" to describe the same "narrower version of a two-width diatonic interval"
- By using the different terms "perfect," "major," and "augmented" to describe the same "wider version of a two-width diatonic interval"

JiMS does not break with tradition lightly. However, JiMS' goal of being the fastest path to deep understanding requires that it break with tradition in this case. By making a clean distinction between the one-width and two-width kinds of diatonic intervals (perfect and imperfect, respectively), and naming the imperfect intervals' narrower and wider qualities consistently (minor and major, respectively), JiMS not only exposes Myhill's Property—arguably the most fundamental pattern in all of Western music—but also reserves the names "diminished" and "augmented" to refer to chromatic alteration of those intervals.

 JiMS-trained musicians are expected to (eventually) learn the traditional interval-naming scheme, in addition to the (more logical) one used by JiMS. However, because JiMS is expected to help students learn music's concepts at roughly three times the speed of traditional methods, JiMS-based students will have ample time to learn the traditional interval-naming scheme, too, and still be way ahead.