{ "openapi": "3.1.1", "info": { "title": "Tuning Reference (String Frequencies \u0026 Temperaments) API", "version": "1.0.0", "summary": "String frequencies for guitar, bass, violin and more at any A4, in equal or historical temperaments.", "description": "Every endpoint performs the same calculation as the human page and returns inputs, result, units, assumptions, sources, warnings and computedAt. MCP endpoint: /mcp." }, "servers": [ { "url": "https://tonegridtuningreference.usefulweb.app" } ], "paths": { "/api/v1/calculate": { "post": { "operationId": "calculate", "summary": "String frequencies for guitar, bass, violin and more at any A4, in equal or historical temperaments.", "description": "Look up the exact frequency of every string of an instrument tuning and of a whole octave of notes for a reference pitch between A4 = 415 and 466 Hz, in equal temperament, 5-limit just intonation, Pythagorean tuning, quarter-comma meantone, Werckmeister III or Vallotti on any tonic — with the deviation of each note from equal temperament in cents. The same tables as the tuner and drone in the Tonegrid app.\n\nMethodology:\n- Equal temperament: f = A4 × 2^((n − 69) / 12) for MIDI note n. Other temperaments shift each pitch class by its deviation from equal temperament, with A held at 0 so that A4 always sounds at the reference pitch, as on tuners with temperament settings.\n- Just intonation (5-limit, asymmetric 12-note scale) uses the ratios 1, 16/15, 9/8, 6/5, 5/4, 4/3, 45/32, 3/2, 8/5, 5/3, 9/5, 15/8 above the tonic. Pythagorean, meantone, Werckmeister III and Vallotti are built from the chain of fifths E♭–G♯: pure fifths (3/2), fifths narrowed by ¼ syntonic comma (meantone), ¼ Pythagorean comma on C–G, G–D, D–A and B–F♯ (Werckmeister III), or ⅙ Pythagorean comma on F–C–G–D–A–E–B (Vallotti).\n- Cents = 1200 × log2(f1 / f2). Frequencies are rounded to 0.001 Hz and cents to 0.01.\n\nReference values. Real instruments also need inharmonicity and string stretch taken into account (pianos are tuned with stretched octaves).", "tags": [ "apps" ], "x-mcp-tool": "tonegrid_tuning_reference", "x-owner-app": "tonegrid", "requestBody": { "required": true, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/TonegridTuningReferenceInput" }, "examples": { "example1": { "summary": "Guitar in standard tuning at A4 = 440 Hz", "value": { "instrument": "guitar/standard", "a4": 440, "temperament": "equal", "tonic": "C", "octave": 4 } }, "example2": { "summary": "Violin at baroque pitch A4 = 415 Hz, Werckmeister III", "value": { "instrument": "violin/standard", "a4": 415, "temperament": "werckmeister3", "tonic": "C", "octave": 4 } }, "example3": { "summary": "Just intonation in D for a D drone, A4 = 442 Hz", "value": { "instrument": "none", "a4": 442, "temperament": "just", "tonic": "D", "octave": 3 } } } } } }, "responses": { "200": { "description": "Calculation result envelope.", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/TonegridTuningReferenceResult" } } } }, "400": { "description": "Malformed JSON body.", "content": { "application/problem+json": { "schema": { "$ref": "#/components/schemas/Problem" } } } }, "422": { "description": "Invalid input (see errors[]).", "content": { "application/problem+json": { "schema": { "$ref": "#/components/schemas/Problem" } } } }, "429": { "description": "Rate limit exceeded (see Retry-After).", "content": { "application/problem+json": { "schema": { "$ref": "#/components/schemas/Problem" } } } } } } }, "/api/v1/tool": { "get": { "operationId": "getToolDefinition", "summary": "Inputs, output schema and examples for this tool", "responses": { "200": { "description": "Tool definition.", "content": { "application/json": { "schema": { "type": "object" } } } } } } } }, "components": { "schemas": { "Problem": { "type": "object", "description": "RFC 9457 problem details. 422 responses include per-field `errors`.", "required": [ "type", "title", "status", "detail" ], "properties": { "type": { "type": "string" }, "title": { "type": "string" }, "status": { "type": "integer" }, "detail": { "type": "string" }, "code": { "type": "string" }, "errors": { "type": "array", "items": { "type": "object", "required": [ "field", "message" ], "properties": { "field": { "type": "string" }, "message": { "type": "string" } } } } } }, "TonegridTuningReferenceInput": { "type": "object", "additionalProperties": false, "properties": { "instrument": { "title": "Instrument tuning", "type": "string", "enum": [ "none", "guitar/standard", "guitar/dropD", "guitar/halfDown", "guitar/dadgad", "guitar/openG", "guitar/openD", "guitar7/standard", "bass4/standard", "bass4/dropD", "bass5/standard", "ukulele/standard", "ukulele/lowG", "ukulele/baritone", "violin/standard", "viola/standard", "cello/standard", "doublebass/standard", "mandolin/standard", "banjo/openG" ], "default": "guitar/standard" }, "a4": { "title": "Reference pitch A4 (Hz)", "type": "number", "minimum": 415, "maximum": 466, "default": 440 }, "temperament": { "title": "Temperament", "type": "string", "enum": [ "equal", "just", "pythagorean", "meantone", "werckmeister3", "vallotti" ], "default": "equal" }, "tonic": { "title": "Tonic (key the temperament is built on)", "type": "string", "enum": [ "C", "C♯", "D", "E♭", "E", "F", "F♯", "G", "A♭", "A", "B♭", "B" ], "default": "C" }, "octave": { "title": "Octave of the note table", "type": "integer", "minimum": 0, "maximum": 8, "default": 4 } }, "required": [] }, "TonegridTuningReferenceResult": { "type": "object", "additionalProperties": false, "required": [ "schemaVersion", "tool", "computedAt", "inputs", "summary", "result", "units", "assumptions", "sources", "warnings", "presentation", "links" ], "properties": { "schemaVersion": { "type": "string", "const": "1.0" }, "tool": { "type": "object", "additionalProperties": false, "required": [ "id", "name", "version" ], "properties": { "id": { "type": "string" }, "name": { "type": "string" }, "version": { "type": "string" } } }, "computedAt": { "type": "string", "format": "date-time" }, "inputs": { "type": "object", "description": "Normalised inputs actually used, including applied defaults." }, "summary": { "type": "string" }, "result": { "type": "object", "additionalProperties": false, "required": [ "a4", "temperament", "tonic", "strings", "notes" ], "properties": { "a4": { "type": "number" }, "temperament": { "type": "string" }, "tonic": { "type": "string" }, "strings": { "type": "array", "items": { "type": "object", "additionalProperties": false, "required": [ "string", "note", "midi", "hz", "centsFromEqual" ], "properties": { "string": { "type": "integer", "description": "1 = lowest-sounding string as listed (string order of the tuning)." }, "note": { "type": "string" }, "midi": { "type": "integer" }, "hz": { "type": "number" }, "centsFromEqual": { "type": "number" } } } }, "notes": { "type": "array", "items": { "type": "object", "additionalProperties": false, "required": [ "note", "midi", "hz", "centsFromEqual", "centsFromTonic" ], "properties": { "note": { "type": "string" }, "midi": { "type": "integer" }, "hz": { "type": "number" }, "centsFromEqual": { "type": "number" }, "centsFromTonic": { "type": "number", "description": "Cents above the tonic within the octave (temperament step)." } } } } } }, "units": { "type": "object", "additionalProperties": { "type": "string" } }, "assumptions": { "type": "array", "items": { "type": "string" } }, "sources": { "type": "array", "items": { "type": "object", "additionalProperties": false, "required": [ "title" ], "properties": { "title": { "type": "string" }, "url": { "type": "string" }, "publisher": { "type": "string" }, "retrievedAt": { "type": "string" }, "note": { "type": "string" } } } }, "warnings": { "type": "array", "items": { "type": "string" } }, "presentation": { "type": "array", "items": { "type": "object" }, "description": "Display blocks used by the human page (same data)." }, "links": { "type": "object", "additionalProperties": false, "required": [ "human", "api", "openapi", "methodology" ], "properties": { "human": { "type": "string", "format": "uri" }, "api": { "type": "string", "format": "uri" }, "openapi": { "type": "string", "format": "uri" }, "methodology": { "type": "string", "format": "uri" } } } } } } } }