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Musical Scales in Ringing

Sets of bells hung for change ringing are commonly described by the weight and note (pitch) of the largest bell (the tenor).  The rest of the notes can be assumed from the convention that the tenor bell is the tonic note of a major scale.  For the convenience of ringers who want to know what those notes would be, the following table lists all of the notes in each of the major scale octaves for all thirteen possible keys.  (F-sharp is the same as G-flat, so there are 13 keys even though there are only 12 notes in a chromatic octave.)  Observe that the table reads left-right from tenor to treble, which is the conventional order for musical scales.  That order also makes this table fit any number of bells, though the "ringing number" in the first header line only fits an octave of bells.  (For more bells than 8, simply repeat to the right.)
Ringing #:  8   7   6   5   4   3   2   1   (8 = tenor; 1 = treble)
Solfege:    Do  Re  Mi  Fa  So  La  Ti  Do
Interval:   1   2   3   4   5   6   7   8   (1 = unison, 8 = octave)
            --  --  --  --  --  --  --  --
Key of Gb:  Gb  Ab  Bb  Cb  Db  Eb  F   Gb  (six flats)
Key of Db:  Db  Eb  F   Gb  Ab  Bb  C   Db  (five flats)
Key of Ab:  Ab  Bb  C   Db  Eb  F   G   Ab  (four flats)
Key of Eb:  Eb  F   G   Ab  Bb  C   D   Eb  (three flats)
Key of Bb:  Bb  C   D   Eb  F   G   A   Bb  (two flats)
Key of F:   F   G   A   Bb  C   D   E   F   (one flat)
Key of C:   C   D   E   F   G   A   B   C   (no flats or sharps)
Key of G:   G   A   B   C   D   E   F#  G   (one sharp)
Key of D:   D   E   F#  G   A   B   C#  D   (two sharps)
Key of A:   A   B   C#  D   E   F#  G#  A   (three sharps)
Key of E:   E   F#  G#  A   B   C#  D#  E   (four sharps)
Key of B:   B   C#  D#  E   F#  G#  A#  B   (five sharps)
Key of F#:  F#  G#  A#  B   C#  D#  E#  F#  (six sharps)

The table above lists the keys in key-signature order from flats to sharps; the table below lists them in alphabetic order from A-flat to G.  Notice that the keys of Gb and F# are identical from a ringer's viewpoint, though different from a musician's viewpoint.

Ringing #:  8   7   6   5   4   3   2   1   (8 = tenor; 1 = treble)
Solfege:    Do  Re  Mi  Fa  Sol La  Ti  Do
Interval:   1   2   3   4   5   6   7   8   (1 = unison, 8 = octave)
            --  --  --  --  --  --  --  --
Key of Ab:  Ab  Bb  C   Db  Eb  F   G   Ab  (four flats)
Key of A:   A   B   C#  D   E   F#  G#  A   (three sharps)
Key of Bb:  Bb  C   D   Eb  F   G   A   Bb  (two flats)
Key of B:   B   C#  D#  E   F#  G#  A#  B   (five sharps)
Key of C:   C   D   E   F   G   A   B   C   (no flats or sharps)
Key of Db:  Db  Eb  F   Gb  Ab  Bb  C   Db  (five flats)
Key of D:   D   E   F#  G   A   B   C#  D   (two sharps)
Key of Eb:  Eb  F   G   Ab  Bb  C   D   Eb  (three flats)
Key of E:   E   F#  G#  A   B   C#  D#  E   (four sharps)
Key of F:   F   G   A   Bb  C   D   E   F   (one flat)
Key of F#:  F#  G#  A#  B   C#  D#  E#  F#  (six sharps)
Key of Gb:  Gb  Ab  Bb  Cb  Db  Eb  F   Gb  (six flats)
Key of G:   G   A   B   C   D   E   F#  G   (one sharp)

Assuming equal temperament, in the major scale, you only need weird things like Cb or E# when in the key of six flats or six sharps, respectively.  Otherwise, they are used (as are double flats or double sharps) only with diminished or augmented intervals, respectively, and those don't occur in normal ringing.  The enharmonic pair F#/Gb is the only one which needs to be considered here, because the enharmonic notes A#, C#, D#, G# are never the tonic notes of major scales, only of minor scales.

There exist a number of unequal temperament tuning schemes, details of which can be found elsewhere on the Web.  In at least some of those temperaments, at least some of the sharp/flat pairs such as F#/Gb are actually distinct notes, and so major scales based on those notes would also be distinct. In that situation, the concept of key signature could readily be extended to seven flats (key of Cb major) and seven sharps (key of C# major).  There being only seven distinct notes in a major scale, this is the limit of the conventional pattern of key signatures; to go farther would require different terminology.  Since the writer of this page is unconcerned with the details of unequal temperament, the determination of the notes and key signatures of such far-out keys is left as an exercise for the unequally-interested reader.


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This page was created 2006/12/08 and last revised 2006/12/09.

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