Sharp or flat? Enharmonic equivalents when notating arpeggios

[Mark H]

I have a question that came up as I was working on arpeggios for the min7flat5 (a.k.a. “half diminished”) in various keys.

So the min7flat5 arpeggio intervals are root, flat3, flat 5, flat 7

For example, the Bmin7flat5 arpeggio is easy, since it contains no sharps or flats:

B, D, F, A

The question comes up when, for example, the root is transposed up to C by one semitone:

C, E flat (a.k.a. D sharp), G flat (a.k.a. F sharp), B flat (a.k.a. A sharp)

What I’m asking is should the correct notation for the first enharmonic note be “E flat”, or “D sharp”? And does this apply to all three flat/sharp notes in the arpeggio? And why?

I’m really just looking for a general guideline so my notation homework is correct, and some idea of why it is so.

Thanks for any assistance folks,

Mark.

[Michael L]

Hi Mark, as I understand this you have to think about what key you’re in. The Cmin7b5 would be the 7th degree in the key of Db…. C being a half-step below Db. In any single key you would not have a C and a C#, it would be C and Db.

So, key of Db is: Db, Eb, F, Gb, Ab, Bb, C, Db
Cmin7b5: C, Eb, Gb, Bb

That’s my take. I think that’s correct, but I’m open to other interpretations.

[Mark H]

Thanks Michael. That gives me something to work with: determine the harmonized scale’s actual key (one fret higher), then figure out the major scale for that key and avoid duplicating note names for the sharps and flats when notating the arpeggio.

I tend to use the minor7flat5 to lead into the V. For example, Cm7flat5 is a great transition chord to an F7 V chord, and then resolving back to a B flat tonic. I had not thought to consider what major scale the Cmin7flat5 belonged to decide whether to designate arpeggio notes as sharp- or flat.

I’ll probably cheat and write them all as flats to save time, since in this arpeggio’s case the notes are all far enough apart to avoid duplicates, within the context of just the arpeggio.

Hope I’ve understood this correctly.

[Jean-Michel G]

Hi,
Michael is correct: Cm7(b5) is the chord built on the leading tone of the Db major scale, so the chord tones have to be
(C Eb Gb Bb).

Enharmonically, the Db major scale is equivalent to the C# major scale: C# D# E# F# G# A# B#.
So, the enharmonic equivalent to Cm7(b5) is the B#m7(b5), whose chord tones are (B# D# F# A#).

You are right, Cm7(b5) -> F7 -> Bb works nicely in terms of voice leading: (C Eb Gb Bb) -> (F A C Eb)
But from a purely theoretical standpoint, this only works because the chord tones in the Cm7(b5) chord are flats and therefore resolve down. If you write (B# D# F# A#) the whole thing would rather resolve up…

[Mark H]

Thanks for that J-M. I’ll be referring back to these posts as I continue diving into theory, particularly as it relates to notating arpeggios and, as an extra benefit, understanding what’s going on within various jazz chord melodies.

I’m finding it opens up the fretboard when I take the time to look at the actual notes & intervals I’m playing instead of only memorizing chord shapes, scales and arpeggio fingerings. I’m also discovering that in my case I have to write things down, and also transpose them to other keys, to really learn the material.

Another thing: the min7flat5 arpeggio works great when improvising, mixes effortlessly with the minor pentatonic. It upgraded my improvisation skills once I realized that.

Appreciate your input guys.

[Jean-Michel G]

Just a few more words while we are at it…

The “min7(b5)” chord isn’t actually a minor chord; it’s often written like one (particularly on jazz lead sheets) and it does have a minor third in it, but it is more properly a diminished triad (R b3 b5) (e.g. B D F) with an additional minor seventh: (R b3 b5 b7), e.g. (B D F A). Its other name, half-diminished, is probably preferable.

Its cousin, the full diminished chord, is a diminished triad with an additional diminished seventh: (R b3 b5 bb7). For example (B D F Ab).

The spelling of these chords is a bit confusing:
– (B D F) = B diminished triad = B°
– (B D F A) = B half-diminished seventh chord = BØ7
– (B D F Ab) = B full diminished seventh chord = BO7
…but “Ø7” and “O7” are written as exponents, which I can’t do in this limited interface.

From a harmonic perspective, you get the half-diminished chord when you harmonize the 7th scale degree of the major scale.
For example, in C major: C D E F G A B -> (B D F A) = BØ7

You obviously also get it when you harmonize the 2nd degree of the natural minor scale: A B C D E F G -> (B D F A).
But if you harmonize the 2nd scale degree of the harmonic minor scale, you get the full diminished chord: A B C D E F G# -> (B D F G#) = (B D F Ab).

The diminished triad, half-diminished seventh chord and full diminished seventh chord all contain a tritone interval (the full diminished chord even contains two tritones!), so they all belong to the Dominant harmonic function group and can be used accordingly… but this is another topic.

[Mark H]

Thanks for the bonus material there J-M

Re. the double flat / double sharp thing, the convention / rule of not having two notes with the same ‘letter’ but extended differently it is now finally making perfect sense to me when considering full diminished. I also appreciate your correct notation of the chord names, “Ø7” for half-, “O7” for full.

The point about the natural minor and harmonic minor scales’ relationships to half diminished and full diminished blows my mind in a good way and is a rabbit hole I intend to go down soon.

Other insight for me when diving into this subject was actually understanding the difference between half diminished and full diminished, viz flatten the last note of the half diminished arpeggio to get to the full diminished. I had to force myself to break apart the arpeggio to get there, not something I naturally have taken the time to do in the past.

My New Year’s Resolution is clear – to get more detail-oriented (notes, intervals) with arpeggios, scales and chords.

For anyone who wants to dive into this, I found this youTube playlist that covers the basics of diminished- and half diminished construction:

[Michael L]

I found this video to be helpful for how to use diminished chords. Not so much on theory, but where they often are found in music. Adam Levy has a “Part 2” on this and one on half-diminished. This one is #93 in his Guitar Tips series. The others are #94 and #95, all on his YouTube channel if you’re so inclined.

[Jean-Michel G]

Not so much on theory, but where they often are found in music.

The theory is rather simple:
– as passing chords, dim chords ares subject to voice leading principles like any other chord
– as functioning chords, they work like a V7 chord.

Any half- or full diminished chord contains at least one tritone (one for the Ø7 and two for the °7); therefore, it resolves exactly like the V7 chord of its key.

In minor keys we need at least the harmonic minor scale since the natural minor scale doesn’t have any leading tone,

Examples:
We are in A major and want to return to the tonic; we can use G#Ø7 -> A

We are in A minor and want to return to the tonic; we can use G#°7 -> A

We are in A major and we want to “tonicisize” the ii chord (Bm).
We can use the secondary diminished coming from the B harmonic minor scale: A#°7 -> Bm

We are still in A major and we want to “tonicisize” the IV chord (D).
We use the secondary diminished in D major: C#Ø7 -> D

…I like Adam Levy a lot, by the way!

[Mark H]

Thanks Michael, I will check those out.

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