Characteristic Intervals Define Chords

‘Harmony’ is defined as, ‘Any simultaneous combination of tones’. (from ‘Dictionary’ on the web).

‘Identity’ is the thing, person, scale, interval, or chord itself without reference to a function.  Scales, intervals, and chords must have their own unique identifiers; M (major), m (minor), x (dominant), Ø (half diminished), and ‘o’ (diminished) in order that they be identified.[1]

‘Function’ is position; nothing more, nothing less, and expressed with numbers; 1-2-3, etc., and I-II-III, etc. Identity and function must not be confused nor combined into a compound symbol.[2]

The major scale and the major chord may be identified by the major 3rd, 6th, and 7th intervals.

The minor scale and chord may be identified by the minor 3rd, 6th, and 7th intervals; referred to as ‘normal’. The major scale is a concatenation of steps and half steps. She is the ‘mother’ of all our music.  From ‘her’ we derive all scales, intervals, and chords that are her ‘children’, each of whom has their own unique identity, regardless of any functional consideration. Jazz harmony utilizes these characteristic intervals in voicings often built with fourths instead of thirds.

The major chord is identified by the major 3rd and the major 7th.  These are its characteristic intervals that give the chord its special, identifiable quality. The minor chord is identified by the minor 3rd and the minor 7th.  These are its characteristic intervals that give the chord its special, identifiable quality.

The dominant chord is identified by the major 3rd and the minor 7th.  ‘V7is not its identifier.  ‘V7’ is a functional indication of a chord built on the fifth note of a scale, and may be of any quality.  ‘V7’ for example is a normal minor chord in a minor key. The dominant as a unique sound quality must have its qualitative identifier in order that it may be hear for what it is; a dominant chord that has no necessary relationship to the fifth note of a scale. All words, for example have more than one definition.  ‘Wall’ board has an entirely different definition then ‘Wall’ street.  ‘Dominant’ the function (V), and dominant the identity (x) have no relationship whatsoever.  ‘Dominant’ must have two different definitions.  One is a position within a scale, the other a sound quality that is identifiable as a unique chord.  The ‘dominant’ as a unique sound quality may be found anywhere in the diatonic or chromatic scale.  The ‘dominant’ as a function (position) is a chord located on the fifth note of any scale and indicated as, ‘V’. Adding ‘7’, as in ‘V7’ adds nothing to its function (position).  Also, ‘V7’ is a compound symbol made up of two numbers.  Numbers do not indicate in any way the identity (quality) of a chord, only its position.

The following is taken from the song, ‘When Sunny Gets Blue’ by Marin Fisher.  The pick-up is on the dominant (V). The dominant (V) usually moves to its tonic (I), but here goes ‘back’ to the super-tonic (II), then to the dominant (V). The second bar shows a minor (m) on the sub-dominant (IV).  The sub-dominant in a major key is normally major (M).  But here it’s a minor chord that moves (progresses) to the dominant (x) on the lowered leading-tone (bVII), that progresses up a step to the tonic (I).[3]  The characteristic intervals of each chord are present in this arrangement. Note that functional indications (positions) are below the staves (I-II-III), etc., and chord qualities (identities) are between the staves.  It works, and works beautifully.  Traditional theory texts cannot handle this.  This is an important illustration of chord function and chord identity.

The following is from the Chopin Nocturne op 9, nr 2.  Measure 20 contains chord functions below the staves, and chord identities between the staves.  I shudder to think how this would be analyzed with traditional harmony and its ‘secondary dominant’ theory.  The second beat of measure 21 contains a dominant sans root (oxm9) over an ‘E-flat’ pedal.  The ‘o’ indicates a missing  root with a minor 9th, ‘m9’.   The diminished chord on ‘D’ represents the upper four notes of the dominant sans root, the major 3rd ‘D’, the 5th ‘F’, the minor 7th ‘A-flat’, and the minor 9th ‘C-flat’.[4]

Ralph Carroll Hedges, B.Ed., B.Mus., M.M.

[1] For some unexplained reason, theorists refuse to acknowledge ‘x’ as the symbol for the identity of the dominant.  Their use of ‘V7’ is a functional indication, not a symbol of the dominant quality.

[2] See ‘Compound Symbols’ by the author.

[3] Note that ‘IV-bVII’ is a Circle progression, and in this case, a ‘half-cadence’, i.e. intransitive.  ‘Cadence’: a place to breath.  The following measure is a new ‘sentence’.  The two must be separated.

[4] The theory of the ‘missing root’ (sum and difference tone) may be found in Helmholtz, ‘On the Sensations of Tone’ pg 152 ff, and Ulehla, ‘Contemporary Harmony’ pg 114 ff, and Giuseppi Tartini, “Trattato di musica secondo la vera scienza dell’armonia'” (Padua, 1754), and on the web, (see ‘Tartini’s tone’ in Wikipedia), also see, ‘sum and difference tones’.

Ralph Carroll Hedges, B.Ed., B.Mus., M.M.

[1] For some unexplained reason, theorists refuse to acknowledge ‘x’ as the symbol for the identity of the dominant.  Their use of ‘V7’ is a functional indication, not a symbol of the dominant quality.

[2] See ‘Compound Symbols’ by the author.

[3] Note that ‘IV-bVII’ is a Circle progression, and in this case, a ‘half-cadence’, i.e. intransitive.  ‘Cadence’: a place to breath.  The following measure is a new ‘sentence’.  The two must be separated.

[4] The theory of the ‘missing root’ (sum and difference tone) may be found in Helmholtz, ‘On the Sensations of Tone’ pg 152 ff, and Ulehla, ‘Contemporary Harmony’ pg 114 ff, and Giuseppi Tartini, “Trattato di musica secondo la vera scienza dell’armonia'” (Padua, 1754), and on the web, (see ‘Tartini’s tone’ in Wikipedia), also see, ‘sum and difference tones’.

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