• OVERVIEW •
A ‘regular’ stack of minor 3rds (i.e. 3 semitones separate each string) – forming a diminished 7th arpeggio [1-b3-b5-bb7] regardless of where you start. These odd symmetrical properties arise because our 12-semitone octave divides neatly into 3 with no remainder – meaning that sequences of 3-fret jumps will always ‘orbit’ back around to (octaves of) the root as you extend the series upwards – i.e. ‘12 semitones=3 frets*4 jumps’, 24=3*8, 36=3*12, and so on. (Thus, Maj. 3rds and Tritone tunings possess similar symmetries, as does the whole-tone scale: as the respective sums 12/4=3, 12/6=2, and 12/2=6 leave no remainders. n.b. It’s easier to visualise these examples as fret-jumping up a single string, rather than dealing with the snakes-and-ladders complexity of switching between them…)
Another aspect of this 3-fretted geometric landscape is that the tuning only spans 1.25 octaves (=15 semitones, as opposed to Standard’s 2-octave, 24-fret range). While this ultra-narrowness may feel melodically constraining, it offers broad access to close-voiced chords and clustered arpeggios (and, of course, diminished sequences, which are produced by literally any single-finger barre chord of three strings or more).
However you may approach it, the layout’s curiosities will certainly give your ear an informative refresh. For one thing, plenty of Western harmony is based on thirds – e.g. jazz chords are generally ‘extended’ by stacking up major & minor thirds, e.g. with jumps of ‘4>3>4>3>4‘. (This is why our naming conventions run over a two-octave span of ‘1-3-5-7-9-11-13’ (=1-3-5-7-2-4-6), rather than the stepwise ‘1-2-3-4-5-6-7’. Thus, we have 9th, 11th, and 13th chords, but no 10th, 12th, or 14th shapes. 6th chords do, however, exist…but whatever, the finer points of these formalisations aren’t so important – it’s all about internalising the sounds!).
Harmony: G/Bb/Db/E dim7 | 1-b3-b5-bb7-1-b3
• TUNING TONES •
• SOUNDS •
Peg-winding theorist Bill Sethares hails the layout’s narrow quirks: “It is a highly compressed tuning, since all six strings are tuned within a tenth [15 frets]. This is about the distance most adults can stretch [with one hand] on a keyboard – and chords tend to be closely voiced, almost keyboard-like. Unlike the piano, however, chords in the minor third tuning often contain multiple copies of a single note…the doubled notes reinforce each other, like the doubled strings of a 12-string guitar add chorusing and depth. When picking or arpeggiating chords, the doubled strings can add a unique percussive effect, and it is easy to play extremely fast mandolin-style picking on adjacent doubled notes”.
Though simple in concept, it rarely sees much 6-string use (partly down to the required re-string). However, similar ‘regular + narrow’ designs do surface among extra-strung guitarists, who can more easily circumvent the issues of restricted range. For example, nightflameauto on the HarmonyCentral forum sets the same sequence on an 8-string [7*3=21 semitone range], whereas Winspear on SevenString describes how “minor 3rds tuning means that a 9-string effectively has the range of a 6-string” [8*3=24]. Also see Said Too Much‘s 7/8/9-string lesson below.
Still, the tuning does occasionally turn up on 6-string, as evidenced by a scattering of online discussions. For example, a fantastic 2013 StackExchange thread contains practical and theoretical insights: “Every 4-note closed form of a major or minor triad, in any inversion, consists of a minor third, a major 3rd, and a perfect 4th, in some order…Any stacked combination of these intervals can be played using four consecutive strings, without fingers having to cross over”…”the top four strings [make] a very nice four-stringed instrument”.
- Thirds Tuning Talk – Said Too Much (2020):
“Bisyllabic speech samples conveying four emotions were recorded…Participants rated the speech samples for perceived emotion, and the use of numerous acoustic parameters as cues for emotional identification was modeled using regression analysis. The minor third was the most reliable cue for identifying sadness…[supporting] the theory that human vocal expressions and music share an acoustic code for communicating sadness…” (From Curtis & Bharucha’s 2010 audiology paper The minor third communicates sadness in speech, mirroring its use in music)
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• 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 Major Thirds: each pair a semitone wider
- All Tritones: doubling the minor third jump
- Iris: a droning two-note minor third configuration
• MORE INFO •
—Further learnings: sources, readings, lessons, other onward links…
- Microtonal minor-ish thirds: Most Western instruments take equally-tempered, ‘300 cent’ minor 3rds (=3 semitones), but there are many other possible shades – check out nearby microtones on Kyle Gann’s Anatomy of an Octave and the Mirahaze Microtonal Encyclopedia: including the ‘Pythagorean’ minor 3rd (=294.135 cents), the ‘overtone’ minor 3rd (=297.513 cents = 19th in the overtone series), the ‘5-limit’ minor 3rd (=315.641 cents), and more
- Octave-slicing symmetries: see Camden Hughes LJS lesson on diminished scales, 12tone’s analysis of Erv Wilson’s The Hexany – and also the late, great jazz virtuoso Pat Martino’s instructional DVD explanations of ‘Parental Forms’ and ‘Dim./Dom.7 Forms’ (“ascent and descent, both in vertical [and] horizontal context…as well as the diminished form in its 5 common groups…”)
Header image: stave-notated stacks of minor 3rds
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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