kennethreitz
ce93f429a2
Publish the Obsidian vault's Knowledge folder as /knowledge (881 notes, 67 folders), with a Knowledge item in the nav and footer. - scripts/import_knowledge.py regenerates data/knowledge from the vault: slugged paths, folder notes as index pages, wikilinks resolved to site links (or plain text), callouts, highlights, and Dataview tables rendered statically. Personal notes are withheld via an exclusion list plus a privacy guard. - tuftecms/core/knowledge.py builds a concept index from note titles and aliases. First mentions on ordinary pages link to their Knowledge note (capped, never in headings, code, links, or sidenotes); Knowledge pages list related notes and where they're mentioned across the site; other pages get a Related Knowledge block. - Knowledge URLs join sitemap.xml (so the sweep test covers them), never displace existing legacy slugs, list alphabetically, and mermaid diagrams render client-side only on pages that have them.
2.5 KiB
description, source
| description | source |
|---|---|
| A trapdoor with four hinges, any of which will open. | obsidian-knowledge |
Diminished Seventh
A trapdoor with four hinges, any of which will open.
The Chord
The diminished seventh is the most rigorously symmetrical chord in tonal music. It stacks three minor thirds in a row, dividing the octave into four perfectly equal parts. On C the notes are C, E♭, G♭, and the double-flatted seventh, A (written B𝄫). Every interval inside it is identical, which means the chord has no fixed root — invert it and it becomes another diminished seventh a minor third away, again and again around the circle.
That symmetry produces maximum instability. The chord contains not one but two tritones, both straining to resolve, and because any of its four notes can act as the root, it can slip toward four different keys with equal ease. It is a knot of pure tension that could untie itself in any direction.
Structure
| Attribute | Value |
|---|---|
| Formula | 1 ♭3 ♭5 ♭♭7 |
| Notes (on C) | C E♭ G♭ A |
| Symbol | C°7 |
| Quality | Fully symmetrical, maximally tense — the pivot chord |
Character
The diminished seventh is dread distilled. It is the chord of silent-film peril and operatic catastrophe, a sound so unstable it seems to vibrate with alarm. Yet its very ambiguity makes it graceful in the right hands — it can twist a passage into a distant key so smoothly that the ear only notices the ground has shifted. Terror and elegance, held in the same four notes.
In Practice
The diminished seventh is music’s great pivot chord. Because it belongs equally to several keys, composers use it to modulate anywhere, sliding between distant tonalities without warning. As a passing chord it links stable harmonies with a jolt of chromatic tension; as a dominant substitute it heightens the pull toward resolution. Romantic composers and jazz players alike prized it. It is the Diminished Triad pushed to its logical extreme, one step past the Half-Diminished Seventh.