The Septimal Intervals
There’s a chord in a barbershop that makes the nerve ends tingle….We might call our chord a Super-Seventh!… How can you detect this chord? It’s easy. You can’t mistake it, for the signs are clear; the overtones will ring in your ears; you’ll experience a spinal shiver; bumps will stand out on your arms; you’ll rise a trifle in your seat. —Art Merill
As I’ve mentioned, the third and the fifth harmonics have been thoroughly studied. In 53-eq, traditional scales and chords can be played and will sound more in tune. As a result, it is possible to create chords and harmonic progressions which are more complex before they dissolve into a puddle of acoustic dissonance. It may also be possible for the ear to hear more distant relationships in a melody because the two distantly related pitches are purely tuned. So the line between complexity and dissonance, between music and noise, can be extended. But the real expansion of our harmonic vocabulary within tonality can come with 53-eq’s ability to evoke the seventh harmonic. The same voicing principles developed over hundreds of years to guide the ear on its harmonic journey through a composition can be extended to septimal harmonies. That’s because the rules of voicing in tonal music are all about revealing harmonic/acoustic relationships from chord to chord and constantly anchoring it to a tonal center. The next logical step in the development of a richer tonal palette comes from applying the tried-and-true techniques of voicing to the septimal tones.
The seventh harmonic has an entirely different “feel” to it. The Pythagorean third harmonic or perfect fifth creates a foundational, stable, powerful affect. The fifth harmonic or just major and minor thirds evoke human emotions of many kinds. The seventh harmonic can evoke deep feelings of despair–as it does in the blues– but also “spaciness,” as well as a feeling of strong musical motion when chord progressions built off the seventh harmonic are employed. If you love Western classical music, you can create music within that tradition that explores entirely new realms. The seventh harmonic can also be downright sexually seductive, as it creates a soundscape that allows escape from the ordinary. It can feel dangerous, ungrounded, haunting. I sometimes call it “emotion squared.” It can also evoke the feeling of being out of your body, floating in some kind of astral plane, even the transition into Death itself. And yet, the seventh harmonic can also bring soothing consonance to once-dissonant intervals (such as the minor seventh or the tritone). In the right composers’ hands, the seventh harmonic can be used to evoke deeply contemplative, restful music. A generation or two of composers exploring the seventh harmonic will yield many more adjectives to describe the expressive potential of this underutilized and underexplored interval.
The seventh harmonic is indeed a whole new musical continent which only a handful of musical pioneers have begun to explore. It is safe to say that tonality can have an entirely new dimension now, and our 21st-century ears can look forward to new musical and theoretical ideas for generations to come. We are the new Haydns and Mozarts.
Let’s take a look at which notes from C can be “septimal,” and how they are derived from the seventh harmonic. The ratios tell us the seventh harmonic is in play. If there’s a septimal seventh going up, the first number in the ratio is a multiple of 7. If there’s a septimal seventh going down (undertone), the second number in the ratio is a multiple of 7. The septimal seventh, the septimal tritone and the septimal minor third are especially evocative, and are commonly heard in the blues. In this list, whenever I say up or down a seventh, I am referring to the 968.8 cents of a septimal seventh interval.
The first and simplest set of five septimal intervals are the 7:4 septimal seventh (a pure seventh up), the Supermajor 8:7 seventh (a pure seventh down), the 7:5 Septimal tritone (a third or fifth-harmonic down plus a seventh up, hence the number 5 in the denominator), the 7:6 Septimal minor third (a fourth plus a seventh), and the 12:7 Septimal major sixth (up a fifth, down a seventh). The [bracketed] sections of these descriptions are the lattice/mandala’s routes to an approximation of each of these intervals in 53-equal. You can hear the harmonic journey and then the actual final intervals in the mp3 file below, as well as being able to read the “scores” for these intervallic journeys.
Figure 14-1 Septimal intervals from C
From C, here are some important “septimal” tones:
C – B1b, 7:4 septimal seventh, seventh up. Evokes spaciness, rest, no urgency to resolve. Very popular among blues singers: a major “blue” note. [approximation: 2 5ths up, 2 3rds up]
C – D1 8:7 septimal supermajor second, seventh down. Evokes a somewhat bright, shimmering quality. [approx. 2 5ths down, 2 3rds down]
C – F1# 7:5 third down, seventh up, septimal tritone (the most consonant tritone there is! Devil’s tritone redeemed?) [approx. 2 5ths up, 1 3rd up]
C – E1b 7:6, 7th up, fifth down, septimal minor third (creates 53-eq comma with two thirds and a fifth up. Profoundly minor-sounding “blue note,” a favorite among blues singers, evokes despair, bottom dropping out) [approx. 5th up, 2 3rds up]
C – A1, 12:7 Septimal major sixth, fifth up, seventh down (also bright, shimmering major feel) [approx. 5th down, 2 3rds down]
If you would like to learn more about this chapter, “Septimal Intervals,” with many more musical examples, you can buy the entire book, The Grand Unified Theory of Music, in pdf form for $25 with hundreds of embedded musical examples of scales and chords from all over the world.
A free introduction to what The Grand Unified Theory of Music offers is on this website and includes both text and a few musical examples from each webpage. If you would like to learn more about this chapter and the full contents of this entire e-book, you can buy The Grand Unified Theory of Music for $25, with hundreds of embedded musical examples of scales and chords from all over the world — and ideas for how to set up your computer system —
You’ll get a personalized password you can use to see the entire e-book. Inside the full book, you will also get a link to the complete pdf file of this e-book, which you can read on your Kindle or similar device. The links to the hundreds of mp3 sound files – the same ones you can hear on the website — will also be included. This is “Version 1.0” of The Grand Unified Theory of Music. Because it is an e-book, additions, corrections and improvements in the sound may be added at any time. The Grand Unified Theory of Music is Copyright © 2018 by Christopher Mohr. All rights reserved.
One person per password. Sharing this password with others is a violation of copyright. Do not allow others to use your password or link to the pdf file!