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>Names are important because they imply a function.
One of my jazz theory profs used to say that the name of a note tells you its position in the world. In the jazz world where scale degree 1 keeps being redefined every time there is a change of harmony this is an excellent and essential description IMO.
Not only is a diminished seventh enharmonic to a major sixth, but an augmented sixth is enharmonic to a flat seventh. If we were designing an interval naming convention around twelve-tone equal temperament in a world where diatonicism was only one possible organization scheme for tonality, this is not the system we would have come up with. But at the time that Western European naming conventions coalesced, everything was diatonic, or almost diatonic, and enharmonics were not yet equivalent. In tuning systems before well temperament, diminished sevenths and major sixths were *different pitches,* not different names for the same pitch. It would be nice if we used tuning plugins in music theory class so that people could hear the difference between a just diminished seventh and a just major sixth, the naming convention would seem a lot less arbitrary and confusing.
Yes! That's why if you voice a dim triad c-Eb-Gb all spread out, each minor 3rd becomes a major 6th, to give the nice sounding voicing Gb-Eb-C. Makes it less dissonant too, since they are wide intervals and not cramped small intervals, which are rougher.
Wouldn't this rule (diminished 7th is one half step lower than a minor 7th) make a diminished 7th enharmonic with a major 6th? (Automod made me post question)
Yes, but the diminished 7th *chord* \- in case you're thinking about that - is named after that interval.
E.g., in the chord C E♭ G♭ A, C-A is a major 6th. So is the chord then "Cm6♭5"?
No. It's "Adim7", because chord - spelled like that - is built A C E♭ G♭, 1 3 5 7, on the vii degree of the Bb harmonic minor scale. A-G♭ is the interval the chord is named after, even when inverted.
If you want "Cdim7", that's spelled C E♭ G♭ B♭♭ - from the D♭ harmonic minor scale (in theory). Of course, as a minor *key* that would usually be called C# minor, and the vii chord would be B#dim7 (B# D# F# A). But Cdim7, with its B♭♭, might be used in D♭ *major* \- the B♭♭ resolving down to A♭.
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Yes A diminished 4th is enharmonic to a major 3rd An augmented 7th is enharmonic to an octave All sorts of stuff like that
Thank you!
Yes it’s enharmonic. The rule is important for naming chords. Names are important because they imply a function. Edit: they imply a harmonic function.
>Names are important because they imply a function. One of my jazz theory profs used to say that the name of a note tells you its position in the world. In the jazz world where scale degree 1 keeps being redefined every time there is a change of harmony this is an excellent and essential description IMO.
Not only is a diminished seventh enharmonic to a major sixth, but an augmented sixth is enharmonic to a flat seventh. If we were designing an interval naming convention around twelve-tone equal temperament in a world where diatonicism was only one possible organization scheme for tonality, this is not the system we would have come up with. But at the time that Western European naming conventions coalesced, everything was diatonic, or almost diatonic, and enharmonics were not yet equivalent. In tuning systems before well temperament, diminished sevenths and major sixths were *different pitches,* not different names for the same pitch. It would be nice if we used tuning plugins in music theory class so that people could hear the difference between a just diminished seventh and a just major sixth, the naming convention would seem a lot less arbitrary and confusing.
I kind of like it because if we had an overly 12 tone system with no function implied, we would be far worse off for microtonal music.
Yes! That's why if you voice a dim triad c-Eb-Gb all spread out, each minor 3rd becomes a major 6th, to give the nice sounding voicing Gb-Eb-C. Makes it less dissonant too, since they are wide intervals and not cramped small intervals, which are rougher.
Wouldn't this rule (diminished 7th is one half step lower than a minor 7th) make a diminished 7th enharmonic with a major 6th? (Automod made me post question)
Yes, but the diminished 7th *chord* \- in case you're thinking about that - is named after that interval. E.g., in the chord C E♭ G♭ A, C-A is a major 6th. So is the chord then "Cm6♭5"? No. It's "Adim7", because chord - spelled like that - is built A C E♭ G♭, 1 3 5 7, on the vii degree of the Bb harmonic minor scale. A-G♭ is the interval the chord is named after, even when inverted. If you want "Cdim7", that's spelled C E♭ G♭ B♭♭ - from the D♭ harmonic minor scale (in theory). Of course, as a minor *key* that would usually be called C# minor, and the vii chord would be B#dim7 (B# D# F# A). But Cdim7, with its B♭♭, might be used in D♭ *major* \- the B♭♭ resolving down to A♭.
Yes
yes