G-B-D-F-G-A
• OVERVIEW •
My ‘squeezed’ sequence of tones 4 to 9 in the harmonic series – if ‘squashed’ to 12-tone equal temperament, they spell out a 9th arpeggio as an ascent-ordered stack of thirds: 1-3-5-b7-9. Bill Sethares’ variant keeps string tension within more sensible bounds, by adding a register-jump in the middle (C-E-G-Bb-C-D). Make up your own!
(To go deeper into the harmonic series, try tuning closer to ‘just intonation’ – the so-called ‘pure’ harmonic intervals. On a cent tuner, the modifications are as follows – B5:-14 | D4:+2 | F3:-31 | A1: +4). Or for extra ear enrichment, you can try tuning to these overtonal shades by ear: see the G Sa-Pa (root-5th) sample on my Tanpuras: Divine Indian Drones page – and my Microtonal Guitar overview.)
Pattern: 4>3>3>2>2
Harmony: G9 | 1-3-5-b7-1-2
• TUNE UP •
[YT]
• SOUNDS •
Unsure if it’s ever been used on record. I imagine Sethares has played around in his shuffling of the same concept, in MIDI format or even acoustically. I’ll re-string & record a demo sometime soon…also send me your experiments and I’ll showcase the best of them!
- Musical Phonology: Overtones – Leonard Bernstein (1974)
• NUMBERS •
| 6str | 5str | 4str | 3str | 2str | 1str | |
| Note | G | B | D | F | G | A |
| Alteration | +3 | +2 | 0 | -2 | -4 | -7 |
| Tension (%) | +41 | +26 | 0 | -21 | -37 | -55 |
| Freq. (Hz) | 98 | 123 | 147 | 175 | 196 | 220 |
| Pattern (>) | 4 | 3 | 3 | 2 | 2 | – |
| Semitones | 0 | 4 | 7 | 10 | 12 | 14 |
| Intervals | 1 | 3 | 5 | b7 | 1 | 2 |
- 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…
- Banjo: also begins with a high-twisted G-B-D across 6-5-4str
- All Minor Thirds: regular arrangement of a similar fundamental
- Flip Thirds (Min): another narrowed conceptual experiment
• MORE INFO •
—Further learnings: sources, readings, lessons, other onward links…
- Sethares’ overtonal variant: the master tuning theorist discusses overtone arrangement on p.48 of his Instrumental Tunings chapter (“Our tempered aural thinking can include tones up to the sixth partial, but beyond that the point the aural perception is merely rational…”)
- More on the overtone series: see my in-depth essay covering the fundamentals of sound and string vibration, included in the World of Tuning’s wider resources – The Impatient Meditation: guitar tuning in fine detail. Although Bernstein is always gonna be a better starting point…
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rāga: ‘that which colours the mind’
George Howlett is a London-based musician, writer, and teacher. I play guitar, tabla, and santoor, loosely focusing on jazz, rhythm, and other global improvised traditions. Above all I seek to enthuse fellow sonic searchers, interconnecting fresh vibrations with the human voices, cultures, and passions behind them. Site above, follow below, & hit me up for…
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