• OVERVIEW •
A ‘regular‘ stack of major 3rds (i.e. 4 semitones separate each string) – forming an augmented triad (1-3-#5) from any of its three notes, regardless of which string you start on. These symmetrical properties arise because our 12-semitone octave divides neatly into 4*3 with no remainder – meaning that sequences of 4-fret jumps will always ‘orbit’ back around to (octaves of) the root as you extend the series upwards – i.e. ‘12 semitones=4 frets*3 jumps’, 24=4*6, 36=4*9, and so on. (Thus, Minor 3rds and Tritone tunings possess similar symmetries, as does the whole-tone scale: because the respective sums 12/3=4, 12/6=2, and 12/2=6 leave no remainders. Top tip: It’s easier to visualise these examples as fret-jumping up a single string (i.e. 0fr, 4fr, 8fr, 12fr…), rather than dealing with the complexities of switching between them.)
Currently the only tuning from all 100+ on the Menu to include two adjacent major 3rds anywhere (…it has five). This looping regularity gives a displaced, un-rooted mood to the open-string harmony. After all, you can’t really say which corner of an equilateral triangle is the most ‘important’, as all three corners give identical support to the others: thus, an octave ‘folded’ into a triangle with sides of length 4 semitones has no natural root [n.b. thanks to reader Bernhard Bloechl for highlighting a previous cut-and-paste error here!]. The same ‘rootless’ property is true of all ‘regular’ interval sequences – e.g. Min. 3rds tuning forms a one-octave ‘square’ with 3-semitone sides, and the circle of 5ths produces a massive, multi-octave, 12-sided ‘dodecagon’ (whereas Tritones tuning would look more like a ‘back-and-forth relay’ between two points, 6 semitones apart).
Harmony: E/Ab/C aug | 1-3-#5-1-3-#5
• TUNING TONES •
• SOUNDS •
Use of the layout has always remained rare, although a few guitarists have explored it in impressive depth. Ralph Patt (1929-2010) started doing so circa 1964, partly via studying the abstruse harmonic concepts of John Coltrane under Gunther Schuller, a student of 12-tone serialism pioneer Arnold Schoenberg – and, correspondingly, this is almost certainly the best tuning for navigating the 12-note chromatic scale, which requires no vertical position-shifting (just ‘0-1-2-3’ on each string…). In Patt’s words, “It makes the hard things easy, and the easy things hard…”
He also sought to counteract the tuning’s narrow range (20 semitones=4 fewer than Standard) by setting it on 7- and 8- string guitars (a usage trend which, for similar reasons, applies to Minor Thirds tuning). See Patt’s own overview of the tuning: including scale patterns, chord sheets, and common progressions (“No finger stretches or shifts are required for any scale, [and] sight-reading becomes easier, because you rarely have to make decisions for what fingerings to use“).
- Ralph Patt captured in action (1955):
“[Major Thirds] is never going to take the place of folk guitar, and it’s not meant to. [But] for difficult music – and for where we are going in free jazz, and even the old bebop jazz – this is a much easier way to play…” (Ralph Patt)
The tuning largely fell from use after Patt’s mid-1970s career switch away from the guitar (he instead become a hydrological geologist: including serving on an independent panel which “slammed the reliability of the [US government] computer models” used to analyse nuclear waste safety). However, it was to resurface several decades later, via the imagination of another extra-strung jazzer – Tony Corman – who derived the tuning independently in the early years of the 21st century:
“While running on a treadmill at the gym, I thought, ‘Of course! 7-string guitar tuned in major 3rds! Same range as [Standard]…no B-string shift, it’s perfect!’ I found a cheap Ibanez solid-body on Craiglist, and started investigating…When it finally occurred to me to fire up a web browser and see if anyone else was working along these lines, I was immediately disabused of any notion of originality…”.
Corman – who originally graduated from Berklee in 1977 as a sax player, before switching to guitar due to focal dystonia affecting his jaw muscles – hails the tuning’s “perfect symmetry…the chromatic scale, whole tone scale, and close voicings are easily accessible…and you run out of guitar less frequently”. Find out more about his intriguing approach on his website – and watch his fantastic demo below, featuring a persuasive array of divine chord voicings.
- What is ‘M3 guitar’? – Tony Corman (2016):
“We are told that we can do anything we put our minds to. It’s not true. I was forced to accept that my woodwind-playing career was over…I considered bailing out of music altogether. That notion lasted about five minutes…I couldn’t thing of anything else that I wanted to do that held a fraction of the attraction…[and] I’d always kinda dug the guitar. I’d played a bit in high school. On the bandstand, I had guitar envy. Those guys could play in any style, had no intonation worries, and the instrument had an appealing logic…” (Tony Corman: How I Lost My Chops)
Andreas Griewank’s 2010 paper Tuning Guitars and Reading Music in Major Thirds (an endeavour “born out of a mathematician’s penchant for regularity, and an amateur guitar player’s longing for simplicity”) suggests note-sets of E-G#-C-E-G#-C and G-B-D#-G-B-D# – while also proposing the name ‘MaThTune’ (‘Major-Thirds-Tuning‘: “It is debatable how the tonal range that now falls one major third short of two octaves should be selected. Starting from the low E one has the advantage that all notes usually expected for the guitar in the music literature are playable…”).
Elsewhere, Bill Sethares’ Altered Tunings Guide discusses the tuning’s chord-formation freedoms (“whenever a chord is played [on] the low C string , it can also be fretted at the same fret on the other C”) – while Migo’s overview describes similar strengths (“Since that day, my relation with the guitar has changed completely…beyond [the] easiness of triads, enriched chords, and transposing…you come to master the chord inversions in a breeze!”). Ole Kirkeby also maintains a website of maj. 3rd-tuned resources (“The main focus is currently on 12-tone rows…an exotic but exciting topic that gets very little exposure elsewhere”).
- End of a Love Affair – Tony Corman’s Morchestra (2017):
“I feel accepted by this instrument in a way I never felt from the woodwinds, and am finally finding simple and genuine joy in playing. So – to all the folks confronted with a similar crossroads – I want you to know that your musical mind is what counts. The instrument is just a manfestation of it…Second acts are where it’s at!” (Tony Corman)
Insights to share? Comment via YouTube, or get in touch!
• NUMBERS •
- See my Tunings Megatable for further such nerdery: more numbers, intervallic relations, comparative methods, etc. And to any genuine vibratory scientists reading: please critique my DIY analysis!
• RELATED •
—Associated tunings: proximities of shape, concept, context, etc…
- All Minor Sixths: doubling the jumps – or inverting them
- All Minor Thirds: shortening the steps by a semitone
- Zigzag Thirds (Maj.): alternating minor and major thirds
• MORE INFO •
—Further learnings: sources, readings, lessons, other onward links…
- Ralph Patt: learn more about the life of the tuning’s original pioneer – who, aside from a storied session career in the 1950s and 60s, helped to edit George Russell’s highly influential Lydian Chromatic Concept of Tonal Organization (which postulates that “all music is based on the tonal gravity of the Lydian mode” [1-2-3-#4-5-6-7]), and, as mentioned above, also worked as an expert hydrological geologist for Oregon’s Department of Water Resources – including serving on an independent panel which “slammed the reliability of the computer models” used to analyse nuclear waste safety by the Department of Energy (in his own words: “Our concern is that the enormous amount of contamination introduced in the soil at Hanford will at some point find its way into the river, and cause us trouble…”)
- Major-ish thirds: Western music generally uses equally-tempered, ‘400 cent’ major 3rds (=4 semitones), but there are many other possible interval shades here: nearby microtones include the ‘Pythagorean schismatic’ third (=384.360 cents), the ‘septimal major third’ (=435.084 cents), and the cult-classic ‘harmonic 5-limit’ third (= 386.314 cents = overtone 5 of the harmonic series) – see many, many more on Kyle Gann’s Anatomy of an Octave, and also check out Roger Ojala’s just intonation-based Major Third Phenomenon on his bespoke-tuned electric keyboard (“I tune by combining *2 & /2 and *3 & /3 and *5 & /5. Because you will find them in all integers up until 7…the 7th harmonic overtone sounds strange…”)
Header image: John Coltrane’s Giant Steps cover art (1960)
George Howlett is a London-based musician, writer, and teacher (guitars, sitar, tabla, & santoor). Above all I seek to enthuse fellow sonic searchers, interconnecting fresh vibrations with the voices, cultures, and passions behind them. See Home & Writings, and hit me up for Online Lessons!
“An intrepid guitar researcher…”
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