Chromatic Dissonant Intervals<\/strong>: These are dissonant intervals formed from the combination of a bass note and accidental tones in the key of the bass note.<\/p>\n Considering that we’ve covered diatonic dissonant intervals<\/a> in earlier posts<\/a>, our focus in this article will be on chromatic dissonant intervals. However, we’ll limit our study to the earliest known chromatic dissonant intervals, which are the augmented fourth<\/em> and the diminished fifth<\/em>.<\/p>\n In the key of C: Here are the two earliest <\/em>chromatic dissonant intervals discovered: The interval above is bigger than the perfect 4th. Therefore, it is called an augmented 4th.<\/strong><\/p>\n <\/p>\n B-F (Diminished 5th)<\/strong> The interval above is smaller than the perfect 5th. Therefore it is called a diminished 5th.<\/strong><\/p>\n The chromatic dissonant Intervals above have something in common. Both of them contain F and B tones.<\/p>\n If we organize the intervals above into quality and quantity, we’ll have:<\/p>\n Quantity<\/strong> – Fourth | Fifth Intervals of the Augmented 4th and Diminished 5th sound unstable<\/em> and tense<\/em>. Perhaps a slight comparison between diminished fifths and perfect fifths will make it plain.<\/p>\n Perfect Fifth:<\/strong> Perfect intervals are called perfect because they do not change their quality when inverted. It’s also important to note that the perfect fifth interval in traditional practice <\/em>is said to be universally stable.<\/p>\n Diminished Fifth<\/strong> The diminished fifth sounds unstable. It is smaller than the perfect fifth by a semitone progression. It involves a relationship between the bass note (B) and a chromatic note (\u266d5) on the B Major scale.<\/p>\n Let’s cover the similarities between the augmented fourth and the diminished fifth. Let\u2019s narrow it down by exploring the relationships these intervals have.<\/p>\n Just like diatonic dissonant intervals<\/a>, chromatic dissonant intervals are related by the simple process of inversion. This relationship bridges the gap between these two dissonant intervals. <\/p>\n Let\u2019s explore these changes in quality and quantity that come from inversion and its effect on chromatic dissonant intervals.<\/p>\n Intervals can be described using numbers that are equivalent to the number of letter names they encompass. Let\u2019s look at the two quantities<\/em> of chromatic dissonant intervals:<\/p>\n Intervals described as fourths<\/strong> span four letter names. For example, F-B<\/strong> spans F, G, A and B. Intervals that encompass five letter names are called fifths<\/strong>.For example, B-F<\/strong> spans B, C, D, E and F. Inversion of these intervals will show us the relationship between these intervals.<\/p>\n Intervals can be inverted using the Octave Transposition Technique<\/a><\/em>. Therefore, fourths like F-B can be inverted by transposing either the melody note an octave lower or transposing the bass note an octave higher.<\/p>\n Approach #1 – Octave transposition of bass note<\/strong><\/p>\n Octave Transposition of F to a higher octave will yield B-F. Approach #2 – Octave transposition of melody note<\/strong><\/p>\n Octave transposition of B to a lower octave will also yield B-F.<\/p>\n B-F encompasses B, C, D, E and F, which is five letter names. Therefore, inversion of a fourth (F-B) will yield a fifth (B-F). <\/p>\n Let’s move on to inversion of fifths<\/em>.<\/p>\n Octave Transposition of the melody note by an octave lower than given or the bass note an octave higher will invert an interval. In the case above (B-F), B is the bass note and F is melody note.<\/p>\n Approach #1 – Octave transposition of bass note<\/strong><\/p>\n Octave transposition of B to a higher octave will yield F-B. Approach #2 – Octave transposition of melody note<\/strong> Having covered the inversion of B-F into F-B, let’s look at the outcome of this inversion. Intervals can be described using adjectives that correspond to their harmonic property. Let\u2019s look at the two qualities of these chromatic dissonant intervals:<\/p>\n Augmented intervals are intervals that are larger than scale tone intervals by a semitone.<\/strong><\/p>\n For example, the quality of the interval F-B, is determined by the major scale of F (which is the bass note). Therefore, considering that B is a semitone higher than B\u266d (which is a scale tone in the major scale of F), the interval between B and F it is described as being “augmented.”<\/p>\n Augment<\/em> is to make larger while diminish<\/em> is to make smaller.<\/p>\n [Tweet “Musicians: Augment is to make larger. Diminish is to make smaller.”]<\/p>\n Therefore F-B is an augmented interval. Diminished intervals are smaller than perfect and minor intervals by a semitone.<\/strong><\/p>\n The quality of the interval (B-F) can be determined with the major scale of B: An interval of a perfect 5th is between the bass note and its 5th scale step (B-F\u266f). The interval we are concerned with (B-F): Therefore, B-F is a diminished<\/em> interval.<\/p>\n So far, we’ve covered two chromatic dissonant interval qualities – Augmented<\/em> and Diminished<\/em>. Let’s look at the outcome of the inversion of these intervals.<\/p>\n The augmented fourth (F-B) is a principal chromatic dissonant interval. It can be inverted by transposing either the melody note an octave lower or transposing the bass note an octave higher. Approach #1 – Octave Transposition of the bass note.<\/strong> Approach #2 -Octave Transposition of the melody note.<\/strong> This gives us a new interval (B-F). Let’s determine its quality.<\/strong><\/p>\n The quality of B-F will be determined with the major scale of B (its new bass note). Considering that B-F is smaller than B-F\u266f by a semitone progression, B-F is described as a diminished<\/em> interval.<\/p>\n Therefore, inversion of an augmented interval will yield a diminished interval.<\/p>\n The diminished fifth (B-F) can be inverted by transposing either the melody note an octave lower or transposing the bass note an octave higher. Approach #1 – Octave Transposition of the bass note.<\/strong> Approach #2 – Octave Transposition of the melody note.<\/strong> Octave transposition of F to a lower octave will also yield F-B.<\/p>\n Now, that we\u2019ve inverted B-F into F-B, what is the quality of F-B?<\/strong><\/p>\n The quality of F-B will be determined with the major scale of F (its new bass note). Our new interval (F-B): Considering that F-B is bigger than F-B\u266d by a semitone progression, F-B\u266d is described as an augmented<\/em> interval.<\/p>\n Therefore, inversion of a diminished interval will yield an augmented interval.<\/p>\n Let\u2019s end by looking at the outcome of the inversion of chromatic dissonant intervals.<\/p>\n Let’s put all that we’ve learned in this article together to see possible harmonic outcomes. In this segment, we’ll do a complete inversion (quality and quantity) of chromatic dissonant intervals. It will seem redundant by now but this is the final step. <\/p>\n Inversion of Quality<\/strong> – Augmented becomes Diminished. If we reverse the process:<\/p>\n Inversion of Quality<\/strong> – Diminished becomes Augmented. The intervals covered in this article are the earliest chromatic dissonant intervals that were discovered. When these intervals were discovered, they were called Diaboli in Musica<\/a><\/em>, which means Devil in Music.<\/em> <\/p>\n These intervals sounded scary and were forbidden in church music because of their extreme dissonance. Over time, things have changed. The devil in music has evolved from being yesterday’s dissonance to today’s consonance<\/a>.<\/p>\nChromatic Dissonant Intervals<\/h2>\n
\n<\/p>\n
\nF-B (Augmented 4th)<\/strong>
\n<\/p>\n
\n<\/p>\n
\nQuality<\/strong> – Augmented | Diminished<\/p>\nStability vs Instability<\/h2>\n
Perfect Fifth vs Diminished Fifths.<\/strong><\/h3>\n
\n<\/p>\n
\n<\/p>\n
What is The Relationship Between an Augmented 4th and a Diminished 5th?<\/h2>\n
Relationship #1 – Quantity<\/strong><\/h3>\n
\n<\/p>\n
\n<\/p>\n
Inversion of Fourths<\/strong><\/h4>\n
\nF<\/strong> is the bass note and B<\/strong> is the melody note.<\/p>\n
\n<\/p>\n
\nGreat Job! We’ve succeeded in inverting F-B into B-F.<\/p>\n“Okay, so what’s the size of B-F?”<\/strong><\/h4>\n
<\/p>\n
Inversion of Fifths<\/strong><\/h4>\n
\n<\/p>\n
\n<\/p>\n
\n
\nOctave transposition of F to a lower octave will also yield F-B.<\/p>\n
\n
\nF-B encompasses F, G, A and B, which is four letter names. Therefore, inversion of a fifth (B-F) will yield a fourth (F-B).<\/p>\nRelationship #2 – Quality<\/strong><\/h3>\n
\n<\/p>\n
\n
\n– larger<\/em> than F-B\u266d (perfect fourth).
\n<\/p>\n
\n<\/p>\n
\n<\/p>\n
\n
\n…is a semitone smaller than the perfect fifth (B-F\u266f).<\/p>\nInversion of Augmented Intervals<\/strong><\/h4>\n
\n
\nF-B<\/strong> – F is the bass note and B is the melody note.<\/p>\n
\n
\nOctave transposition of F to a higher octave will yield B-F.<\/p>\n
\n
\nOctave transposition of B to a lower octave will also yield B-F.<\/p>\n
\n
\nOur new interval (B-F):
\n
\n…is closer to the perfect fifth (B-F\u266f) in the key of B. Same letters.
\n<\/p>\n
Inversion of Diminished Intervals<\/strong><\/h4>\n
\n
\nB-F<\/strong> – B is the bass note and F is the melody note<\/p>\n
\n
\nOctave transposition of B to a higher octave will yield F-B.<\/p>\n
\n<\/p>\n
\n<\/p>\n
\n
\n…is closer to the perfect fourth (F-B\u266d) in the key of F. Same letters.
\n<\/p>\n
\n2nd Relationship<\/strong> \u2013 All Augmented and Diminished intervals are related by inversion of quality<\/strong>.<\/div>\nInversion of the Augmented Fourth and the Diminished Fifth<\/h2>\n
Inversion of an Augmented 4th<\/strong><\/h3>\n
\nInversion of Quantity<\/strong> – 4th becomes 5th.
\n**Inversion of an Augmented 4th yields a Diminished 5th.<\/p>\nInversion of a Diminished 5th<\/strong><\/h3>\n
\nInversion of Quantity<\/strong> – 5th becomes 4th.
\n**Inversion of a Diminished 5th yields an Augmented 4th.<\/p>\nDiabolus in Musica<\/h2>\n