Rango's Dog House

I received some feedback about the Interactive Circle of Fifths on Facebook. I decided to take the conversation to Claude Opus 4.5. The following is my conversation verbatim. It reveals a depth of reasoning that is astounding, and provides guidance for next steps. For an introduction to the online tool, refer to the About page.

The conversation:

I have some feedback regarding the Inner Ring. I’m not sure it’s working how people might expect, with regards to the diminished scales. For the Cmaj/Amin wedge, what is the appropriate scale to display? It’s currently showing Bdim because that’s the chord. However an argument could be made that it should be something else (I think Cdim). This was the feedback:

The feedback:

What is the inner circle supposed to be exactly? The whole half symmetric? It’s in the wrong spot on the circle. The one at 12 o’clock would occur at 9 o’clock Eb/C minor over a G13b9 spelled as: G Ab Bb (B nat) C# D E F. It would have a dominant function over G (V7), using Bº7 and C#º7 as upper structure both tensions as upper and lower leading tones pointing toward C tonic, but the MINOR version not the major version. Without a tonal context (5 in the bass) the symmetrical scale is ambiguous just like a chromatic or whole tone scale would be. The scale that should be in the C/A minor family 12 o’clock should be rooted “E F G G# A# B C# D”. At 3 o’clock here.

My response:

The layout is simple, the diminished chord in Cmaj is Bdim. The scale can be toggled and it’s Bdim as people would expect. I don’t understand why you would want to deviate from that. It makes sense as it is even if there are other ways to express the inner ring.

His follow-up:

The B diminished chord in C major is a half diminished. BDFA. The purpose of the “diminished scale” is that it derives from the FULLY diminished 7, from the raised 7th degree from C MINOR. Bb->B natural gives BDFAb. The variable 7th is even a part of the actual scale for this reason, you get to use both notes. You have the scales associated with the wrong key signatures inside the circle. The extra symmetrical “out notes” are accidentals against the minor key’s key signature.

Can you make sense of his feedback? Is the current behavior what a someone deeply familiar with music theory would expect?

Claude’s Response:

This is a deep music theory question. Let me parse through the feedback carefully.

The user’s friend is making a sophisticated point about diminished scales and their harmonic function. Let me break it down:

Current Implementation:

• For C major/A minor wedge, we show B diminished scale (B C# D E F G Ab Bb)
• This is based on the vii° chord in C major being B°

Half-diminished vs Fully diminished distinction:

In C MAJOR, the naturally occurring vii chord is B half-diminished (B-D-F-A) – also written Bø or Bm7♭5

The FULLY diminished seventh (B-D-F-Ab) comes from C HARMONIC MINOR (which has B natural, not Bb)

The diminished scale (whole-half or half-whole symmetric) is specifically associated with the FULLY diminished 7th chord

The scale’s harmonic function:

The diminished scale has dominant function – it resolves somewhere

The scale built on B (B C# D E F G Ab Bb) functions as a dominant over… not C major, but rather as part of a V7 chord

The friend is saying this scale should be associated with the key it RESOLVES to, considering its dominant function

What scale should be at C/Am?

The friend suggests “E F G G# A# B C# D” should be at the C/Am position

This is the E diminished scale (half-whole)

Why? Because E°7 (E-G-Bb-Db, enharmonically E-G-A#-C#) is actually a rootless G7b9, which resolves to C minor

Let me think about this more carefully…

In jazz theory:

• A diminished 7th chord built on the leading tone (B in C) is called vii°7
• The chord’s complex structure reveals its powerful harmonic potential
• It functions as a dominant substitution with incredible tension and resolution

The diminished scale’s symmetrical nature allows for multiple interpretations. Its half-whole mode creates tension that wants to resolve, essentially acting as a sophisticated dominant chord generator. The scale’s chromatic inflections provide rich harmonic possibilities across different musical contexts.

The diatonic half-diminished chord in C major (B-D-F-A) differs from the fully diminished B°7 chord. This distinction matters because it changes how the chord functions within the harmonic progression. The scale choice depends on the specific harmonic intent – whether creating tension, preparing resolution, or exploring chromatic substitutions.

The key insight is understanding how these theoretical approaches – traditional and jazz functional harmony – offer different lenses for analyzing the same musical material. Each perspective reveals unique aspects of the chord’s potential and its role in harmonic movement. The B°7 chord in C harmonic minor serves as a dominant leading to Cm, highlighting the scale’s unique harmonic structure.

Examining the C/Am wedge reveals multiple potential diminished scale perspectives: C major’s Bø7, A minor’s G#°7, and C minor’s B°7. Each context offers a different harmonic interpretation.

The proposed E half-whole diminished scale demonstrates fascinating symmetry, connecting to multiple diminished seventh chords across different enharmonic equivalents. Its intricate relationships reveal the complex interconnectedness of harmonic systems.

A closer look at the current implementation shows discrepancies in scale placement and root selection, suggesting a need for careful recalibration of the theoretical framework.

The friend’s proposed scale follows a precise half-whole diminished pattern starting from E, with specific interval relationships that differ from our current configurations. I’m tracking the unique intervallic structure: half-whole-half-whole-half-whole-half-whole, which creates a distinct harmonic landscape.

This scale’s unique construction implies potential shifts in our current musical mapping, particularly around the C/Am and related harmonic regions.

The symmetric nature of the diminished scale suggests multiple valid interpretations, with each chord potentially serving multiple functional roles depending on harmonic context. The E°7 chord exemplifies this complexity, revealing potential resolutions to F, F#, and other tonal centers.

The core insight emerges from the scale’s inherent ambiguity – its symmetric structure allows multiple theoretical perspectives, challenging straightforward categorization.

Two primary approaches emerge: the scale-degree method versus functional harmony interpretation. While the scale-degree approach offers pedagogical clarity by associating the diminished scale with the seventh scale degree, the functional harmony perspective emphasizes harmonic resolution and contextual meaning.

The current implementation provides a consistent, learner-friendly framework, but risks oversimplifying the nuanced relationships within diminished harmony.

For an educational tool targeting musicians at different skill levels, maintaining the straightforward approach while acknowledging the complexity for advanced practitioners seems most effective. The goal is to balance accessibility with theoretical depth, allowing musicians to grasp foundational concepts before exploring more intricate harmonic relationships.

Claude’s Summary:

Your friend raises valid points from a jazz/functional harmony perspective. Let me break down the theoretical disagreement:

The Core Issue: Half-diminished vs Fully-diminished

Your friend is correct that in C major, the diatonic vii chord is actually B half-diminished (Bø7): B-D-F-A. This uses only notes from the C major scale.

The fully diminished B°7 (B-D-F-Ab) comes from C harmonic minor (C-D-Eb-F-G-Ab-B), where the raised 7th degree creates the leading tone.

The diminished scale (the symmetric whole-half or half-whole pattern) is specifically associated with fully diminished 7th chords, which arise from minor keys, not major.

Two Valid Approaches:

Approach	Logic	At C/Am wedge
Current (scale-degree)	Show diminished scale on the 7th degree of the major key	B dim scale
Functional harmony	Show the diminished scale that resolves to this key (from its dominant function)	Different association

Your friend’s specific argument:

The diminished scale functions as a dominant — it wants to resolve somewhere. The B°7 chord (and its associated scale) functions as part of G7b9, which resolves to C minor, not C major. So showing B diminished scale at the C/Am wedge conflates major and minor in a way that’s theoretically inconsistent.

My assessment:

Your current implementation is pedagogically sound and consistent — it follows a simple rule (7th degree = diminished) that’s easy to understand. Many circle of fifths tools take this approach.

However, your friend is right that a jazz theorist might expect different behavior, since the diminished scale’s natural harmonic context is minor keys with dominant function.

Options:

1. Keep as-is — It’s consistent and educational for most users
2. Change association — Base it on the relative minor’s vii°7 (would put G#° at C/Am since G# is vii of A minor)
3. Add explanation — Note in the UI that this shows the “leading tone diminished” which has dominant function toward the minor key

Would you like me to explore option 2, or do you prefer keeping the current straightforward approach?

Resolution:

Based on Claude’s analysis, I’ve decided to add menu to the UI. When a diminished scale is selected the control will become active, allowing the user to switch between Scale Degree / Harmonic Function / Minor Tonic. This supports more advanced users while keeping the default workflow as simple as possible.