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Regular Tuning

A multi-string tuning with the same directed pitch interval between every pair of adjacent open strings.

Version
v1 · 2026-10-03 · History
Domain-specific #
13566
Domain group
Arts & Aesthetic Practice
Origin domain
Music & Musicology
Subdomains
String Instrument Tuning, Guitar Performance → Music & Musicology
Aliases
Regular guitar tuning

Core Idea

A regular tuning assigns an equal directed musical interval between every adjacent pair of open strings on a multi-string instrument. In a six-string guitar all-fourths tuning, for example, the open pitches E–A–D–G–C–F rise by five semitones at each crossing. Major-thirds tuning uses four semitones between each pair. What recurs is the between-string pitch step; neither a particular starting note, a particular interval size, nor the presence of frets defines the family.[1]

Equal string spacing makes a feasible fingering pattern translatable across neighboring sets of strings while preserving its internal pitch intervals; each one-string move transposes the sounding pattern by the common interval. This must not be confused with sliding a fretted shape along the neck: moving every played fret by the same amount transposes a shape in standard tuning too. Regularity supplies the across-string invariance, not the ordinary along-fret invariance.[1]

Structural Signature

Sig role-phrases:

  • Ordered open strings — The instrument has adjacent strings with assigned open pitches. A single interval or fretted scale without this sequence is not a tuning of the stated kind.
  • Constant adjacent interval — The directed pitch difference from one open string to the next is the same throughout. One exceptional crossing breaks the defining rule, as in standard E–A–D–G–B–E.[2]
  • Fretboard mapping — In the ordinary equally fretted setting, moving by one fret shifts any string by one semitone. This independent fact lets the equal string step be compared with finger patterns.
  • Across-string transposition — A playable pattern shifted to neighboring strings retains relative intervals and changes absolute pitch by the constant step. This is a derived affordance within string and fret limits, not an extra tuning criterion.[1]

What It Is Not

  • Not any alternate tuning. An open-chord tuning can change several strings without making all adjacent intervals equal.
  • Not the same as scordatura. Scordatura is a deliberate departure from an instrument's prevailing standard for performance; regular tuning is a structural open-string assignment, whether new, customary, or built into an instrument.
  • Not a guarantee of easy chords. A uniform grid can complicate familiar six-string voicings; Sethares notes a shortage of easy full six-string major/minor chords in all-fourths tuning.[1]
  • Not simply movable barre chords. Along-fret transposition works in standard tuning as well; it does not test between-string regularity.[1]

Scope of Application

Regularity is useful when a player or arranger wants a consistent relation among string crossings. All-fourths, major-thirds, minor-thirds, and all-fifths patterns give different open-string spans and voicing possibilities while sharing the equal-step rule.[1] The choice of interval affects ergonomics, available range, repeated pitch classes, and open-string chords. It does not imply a universally superior tuning.

This entry uses the ordinary guitar-like fretboard setting to explain fingering consequences. The identity itself is about adjacent open pitches; fretless instruments, microtonal fretting, and nonuniform fret systems need an explicit interval convention before the same shape-translation inference is made.

Clarity

Let \(p_i\) be the semitone-number pitch of open string \(i\), ordered low to high. The tuning is regular when \(p_{i+1}-p_i=c\) is the same directed interval \(c\) for every adjacent pair. In ordinary equal-tempered fretting, the pitch at fret \(f\) is \(p_i+f\), so moving a playable shape one string higher adds \(c\) to every note; moving it \(k\) frets higher adds \(k\) in any tuning. These distinct symmetries are easily conflated. They also assume enough strings and frets remain for the moved fingering.

Manages Complexity

Instead of memorizing a different interval adjustment at each string boundary, a player can reason from one step \(c\). A pattern that crosses strings can be reused on another group without rebalancing the exceptional standard-tuning G–B interval. The simplification is local to pitch geometry: hand stretch, string gauge, open strings, and the sound of doubled notes still matter. A three-string major-thirds pattern can repeat pitch classes an octave later, whereas the all-fourths layout spreads pitches differently.[1][2]

Abstract Reasoning

If each adjacent open-string difference is \(c\), then \(p_i=p_0+ic\). For a fretted shape with notes \((i_j,f_j)\), the pitches are \(p_0+i_jc+f_j\). Replacing every \(i_j\) by \(i_j+1\) yields \(p_0+i_jc+f_j+c\): all internal intervals are unchanged and the chord transposes by \(c\). Replacing every \(f_j\) by \(f_j+k\) also transposes by \(k\), but that second fact needs no constant \(c\). Pitch classes repeat after the smallest positive \(n\) with \(nc\) divisible by 12; in the cited major-thirds instance \(n=3\), provided that many strings exist.[1]

Knowledge Transfer

To evaluate another tuning, list the open pitches and compute every adjacent directed interval. If they agree, assess what cross-string shapes and open voicings become available; if they do not, identify where a fingering must change. The equal-step reasoning transfers across all-fourths and major-thirds layouts, but exact chord shapes, string gauges, and physical reach do not. An interval pattern that is mathematically regular may be impractical for a particular instrument or repertoire.[1]

Examples

All-fourths guitar

E–A–D–G–C–F places a perfect fourth between each adjacent pair. A feasible four-string voicing can move to the next four strings with its relative fingering preserved, sounding a fourth higher. Sethares presents cross-string chord moves and also notes practical full-six-string voicing limits.[1]

Mapped back: Ordered open strings → E–A–D–G–C–F; Constant adjacent interval → five semitones; Fretboard mapping → identical fret numbers have identical offsets on each string; Across-string transposition → one-string move preserves pattern and raises it a fourth where playable.

Major-thirds guitar

C–E–G♯–C–E–G♯ uses four semitones per crossing. A same-position fingering shifted one string rises by a major third; moving three strings repeats its pitch classes an octave higher when the fingering fits the remaining strings. Sethares discusses both cross-string moves and the compressed, repeated-note character of this tuning.[1]

Mapped back: Ordered open strings → C–E–G♯–C–E–G♯; Constant adjacent interval → four semitones; Fretboard mapping → a fixed fret offset adds to each open pitch; Across-string transposition → one-string major-third shift and three-string octave pitch-class repetition, within instrument bounds.

Structural Tensions

  • Transferable fingering versus familiar voicings. Uniform crossings let patterns move across strings, while standard tuning's irregular third supports familiar open and six-string chord shapes. A player can gain geometric reuse but lose a favored voicing. Diagnostic: Which target chords actually become easier or harder on the chosen instrument?[1][2]
  • Compact intervals versus overall range. With a fixed number of strings, a smaller common step crowds open pitches and may double chord notes, while a larger one expands range and can make adjacent-note shapes wider. Neither goal can be maximized independently of the other. Diagnostic: Does the repertoire call for close voicings or broad bass-to-treble span?[1]

Structural–Framed Character

Regular Tuning is mixed-structural: adjacent open-string pitches follow an equal interval rule, but which pitches and instruments are considered is framed by musical practice. Its evaluative weight is low in the definition; “regular” does not mean musically superior, and a tuning's usefulness depends on repertoire and technique. It is human-practice-bound because strings, pitch systems and tuning choices are made and learned; the equal-step relation is formal once those choices are fixed. Its institutional origin lies in string-instrument practice and theory, not in one manufacturer's standard. Its vocabulary travel reaches other ordered sets of tuned strings that satisfy the same pitch-interval relation, while fret layout and finger geometry do not travel automatically. Import versus recognition requires comparing successive open-string intervals; a visually regular chord chart or equal fret spacing alone is not the identity.

Live Symmetry names a related portable constant-step pattern, but the current draft does not assert it as a strict parent of a pitch assignment. A possible future-prime candidate is constant-step assignment along ordered positions, to be tested separately across substrates; the named tuning remains a musical instance. Its character: a chosen pitch-sequence arrangement with an exact interval test and instrument-specific affordances that do not make the tuning itself a universal prime.

Structural Core vs. Domain Accent

This distinguishes the interval relation from the particular musical instrument that realizes it.

What is skeletal. Assign values to ordered positions so each neighboring pair has the same directed step. That is a possible future-prime candidate; live Symmetry illuminates the repetition but is not asserted as a genus for this pitch assignment. The thin relation can be discussed outside music, but it does not by itself produce a playable tuning.

What is domain-bound. The positions are an ordered sequence of open strings and the repeated step is a musical pitch interval under the chosen tuning system. Remove open-string pitch assignments and the arrangement is no longer regular tuning, however uniform its visual spacing. Guitar-specific six-string layout, the semitone fret lattice, a standard-tuning contrast and ergonomic limits affect uses and fingering patterns. Equal intervals permit across-string shape translation under suitable fretboard assumptions; they do not uniquely determine along-neck transposition, which ordinary regular fretboards allow under broader conditions, nor guarantee every shifted fingering is playable.

Why this is not a prime. Constant-step structure might have broad reach, but its prime status is unadjudicated and Symmetry already carries some of the general insight. Regular tuning is recognized on string instruments when the open-string interval test holds. Applying its name to a uniform scheduling grid imports an analogy while losing pitches and strings. The instrument identity stays in music even though its structural skeleton can be abstracted for comparison.

Symmetry is a conceptual neighbor: the repeated string step gives a translation symmetry of the pitch layout. It is not added as a strict parent because regular tuning is a pitch assignment, not a symmetry object in every catalog sense. The live Pitch Interval entry concerns a relation between two octave-specified pitches; this entry constrains a sequence of such relations. Scordatura concerns the performance act of departing from a prevailing tuning, not the equal-step genus. No defensible existing parent is asserted.

Neighborhood in Abstraction Space

Regular Tuning sits in a sparse region of the domain-specific corpus (78th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Music Theory Concepts & Notation (20 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-08

Not to Be Confused With

Standard guitar tuning has E–A–D–G–B–E open pitches, with four fourths and one major third; that single exception prevents equal across-string transposition through the G–B boundary.[2] A tuning that repeats pitch classes after a few strings is a special arithmetic case of regularity, not the definition. A chord played one fret higher is transposed regardless of the string tuning; it does not demonstrate this entry's distinctive across-string relation.

References

[1] William A. Sethares, “Regular Tunings”, in The Alternate Tuning Guide, printed pp. 52–67. Author-hosted University of Wisconsin PDF directly checked for definition, all-fourths and major-thirds examples, cross-string moves, and voicing limitations. registry ↩a ↩b ↩c ↩d ↩e ↩f ↩g ↩h ↩i ↩j ↩k ↩l ↩m

[2] Jeff Owens, “Standard Tuning: How EADGBE Came to Be”, Fender. Manufacturer article directly checked for the open-string interval sequence; historical and ergonomic claims beyond that sequence are not relied upon. registry ↩a ↩b ↩c ↩d