Repetitive tuning

Repetitive tunings are a type of alternative tunings for the guitar. A repetitive tuning begins with a list of notes that is duplicated, either at unison or at higher octaves.

Among regular tunings, there are four repetitive-tunings (besides trivially repetitive tunings such as C-C-C-C-C-C); this article discusses three minor-thirds tuning, major-thirds tuning, and augmented-fourths tuning (but not major seconds tuning, which is not repetitive on six strings). Among open tunings, there are repetitive versions of open C tuning and open G tuning, which have been associated with the English and Russian guitars, respectively.

Repetition eases the learning of fretboard and chords and eases improvisation. For example, in major-thirds tuning, chords are raised an octave by shifting fingers by three strings on the same frets.^[2]

Repetitive tunings are listed after their number of open pitches. For example, the repetitive open-C tuning C-E-G-C-E-G has three open-pitches, each of which is associated with repeated notes {(C,C), (E,E), (G,G)}.

The trivial tuning repeats the same note every string. It is also called a unison regular tuning.

C-C-C-C-C-C.^[3]

Other trivial-tunings repeat their single notes on a higher octave (or on higher octaves), for example,

C-C-c-c-c'-c'.

The following tunings repeat their notes on a higher octave after two strings:

• Augmented-fourths tuning, for example, B-F-b-f-b'-f'.

Any note fingered on one string can be fingered on two other strings. Thus chords can be fingered in many ways in augmented-fourths tuning. It is also a regular tuning in which the interval between its strings is a tritone (augmented fourth).^[4]

• A cittern tuning, such as C-G-c-g-c'-g'.^[5]

There are other tunings for the cittern.^[6]

• Alternating fourths and fifths tuning, such as A1-D2-A2-D3-A3-D4. (ADADAD)

This kind of tuning can also be called modal D or open D5 as it contains a D chord without a third. It is also used on other instruments, e.g. fiddle, mandolin and the Irish bouzouki.

The following tunings repeat their notes after three strings:

• Major-thirds tuning, such as E-G♯-c-e-g♯-c' and

D♯-G-B-D♯-G-B-D♯,^[7]

Chord inversion is especially simple in major-thirds tuning. Chords are inverted simply by raising one or two notes three strings. The raised notes are played with the same finger as the original notes. The major-thirds tuning is also a regular tuning having a major third interval between strings.^[1][2]

• Open G tuning, which is used as D', G', B, D, g, b, d' for the (7-string) Russian guitar.^{[8][9][10][11]}
• Open C tuning.^[12] For the English guitar's open C tuning,^[13] there are ten strings—of which the highest eight are paired in four courses (duplicated strings), C E GG cc ee gg.

In each minor-thirds tuning, every interval between successive strings is a minor third. It repeats its open-notes after four strings. Doubled notes have different sounds because of differing "string widths, tensions and tunings, and [they] reinforce each other, like the doubled strings of a twelve string guitar add chorusing and depth," according to William Sethares.^[14]

In the minor-thirds tuning beginning with C,

C-D♯-F♯-a-c-d♯

the open strings contain the notes (c, d♯, f♯) of the diminished C chord. The minor-thirds tuning is also a regular tuning, which has a minor third interval between consecutive strings.^[14]

• Scordatura, alternative tunings of stringed instruments
• Stringed instrument tunings

• Griewank, Andreas (1 January 2010), Tuning guitars and reading music in major thirds, Matheon preprints, vol. 695, Berlin: DFG research center "MATHEON, Mathematics for key technologies" Berlin, MSC-Classification 97M80 Arts. Music. Language. Architecture. Postscript file and Pdf file, archived from the original on 8 November 2012
• Sethares, William A. (2011). "Alternate tuning guide". Madison, Wisconsin: University of Wisconsin; Department of Electrical Engineering. 2010 PDF version by Bill Sethares. Retrieved 19 May 2012.