diff --git a/package-lock.json b/package-lock.json
index ad75e6b2..4e5a099a 100644
--- a/package-lock.json
+++ b/package-lock.json
@@ -9,6 +9,7 @@
       "version": "2.0.1",
       "dependencies": {
         "jszip": "^3.10.1",
+        "mathjs": "^11.5.0",
         "moment-of-symmetry": "github:xenharmonic-devs/moment-of-symmetry#v0.2.1",
         "qs": "^6.11.0",
         "scale-workshop-core": "github:xenharmonic-devs/scale-workshop-core#v0.0.1",
@@ -53,11 +54,11 @@
       }
     },
     "node_modules/@babel/runtime": {
-      "version": "7.19.4",
-      "resolved": "https://registry.npmjs.org/@babel/runtime/-/runtime-7.19.4.tgz",
-      "integrity": "sha512-EXpLCrk55f+cYqmHsSR+yD/0gAIMxxA9QK9lnQWzhMCvt+YmoBN7Zx94s++Kv0+unHk39vxNO8t+CMA2WSS3wA==",
+      "version": "7.20.7",
+      "resolved": "https://registry.npmjs.org/@babel/runtime/-/runtime-7.20.7.tgz",
+      "integrity": "sha512-UF0tvkUtxwAgZ5W/KrkHf0Rn0fdnLDU9ScxBrEVNUprE/MzirjK4MJUX1/BVDv00Sv8cljtukVK1aky++X1SjQ==",
       "dependencies": {
-        "regenerator-runtime": "^0.13.4"
+        "regenerator-runtime": "^0.13.11"
       },
       "engines": {
         "node": ">=6.9.0"
@@ -1374,6 +1375,18 @@
         "node": ">=4.0.0"
       }
     },
+    "node_modules/complex.js": {
+      "version": "2.1.1",
+      "resolved": "https://registry.npmjs.org/complex.js/-/complex.js-2.1.1.tgz",
+      "integrity": "sha512-8njCHOTtFFLtegk6zQo0kkVX1rngygb/KQI6z1qZxlFI3scluC+LVTCFbrkWjBv4vvLlbQ9t88IPMC6k95VTTg==",
+      "engines": {
+        "node": "*"
+      },
+      "funding": {
+        "type": "patreon",
+        "url": "https://www.patreon.com/infusion"
+      }
+    },
     "node_modules/concat-map": {
       "version": "0.0.1",
       "resolved": "https://registry.npmjs.org/concat-map/-/concat-map-0.0.1.tgz",
@@ -1566,10 +1579,9 @@
       }
     },
     "node_modules/decimal.js": {
-      "version": "10.4.2",
-      "resolved": "https://registry.npmjs.org/decimal.js/-/decimal.js-10.4.2.tgz",
-      "integrity": "sha512-ic1yEvwT6GuvaYwBLLY6/aFFgjZdySKTE8en/fkU3QICTmRtgtSlFn0u0BXN06InZwtfCelR7j8LRiDI/02iGA==",
-      "dev": true
+      "version": "10.4.3",
+      "resolved": "https://registry.npmjs.org/decimal.js/-/decimal.js-10.4.3.tgz",
+      "integrity": "sha512-VBBaLc1MgL5XpzgIP7ny5Z6Nx3UrRkIViUkPUdtl9aya5amy3De1gsUUSB1g3+3sExYNjCAsAznmukyxCb1GRA=="
     },
     "node_modules/deep-eql": {
       "version": "3.0.1",
@@ -2041,6 +2053,11 @@
         "node": ">=12"
       }
     },
+    "node_modules/escape-latex": {
+      "version": "1.2.0",
+      "resolved": "https://registry.npmjs.org/escape-latex/-/escape-latex-1.2.0.tgz",
+      "integrity": "sha512-nV5aVWW1K0wEiUIEdZ4erkGGH8mDxGyxSeqPzRNtWP7ataw+/olFObw7hujFWlVjNsaDFw5VZ5NzVSIqRgfTiw=="
+    },
     "node_modules/escape-string-regexp": {
       "version": "4.0.0",
       "resolved": "https://registry.npmjs.org/escape-string-regexp/-/escape-string-regexp-4.0.0.tgz",
@@ -3262,6 +3279,11 @@
       "integrity": "sha512-Yljz7ffyPbrLpLngrMtZ7NduUgVvi6wG9RJ9IUcyCd59YQ911PBJphODUcbOVbqYfxe1wuYf/LJ8PauMRwsM/g==",
       "dev": true
     },
+    "node_modules/javascript-natural-sort": {
+      "version": "0.7.1",
+      "resolved": "https://registry.npmjs.org/javascript-natural-sort/-/javascript-natural-sort-0.7.1.tgz",
+      "integrity": "sha512-nO6jcEfZWQXDhOiBtG2KvKyEptz7RVbpGP4vTD2hLBdmNQSsCiicO2Ioinv6UI4y9ukqnBpy+XZ9H6uLNgJTlw=="
+    },
     "node_modules/jazz-midi": {
       "version": "1.7.6",
       "resolved": "https://registry.npmjs.org/jazz-midi/-/jazz-midi-1.7.6.tgz",
@@ -3666,6 +3688,28 @@
       "integrity": "sha512-CkYQrPYZfWnu/DAmVCpTSX/xHpKZ80eKh2lAkyA6AJTef6bW+6JpbQZN5rofum7da+SyN1bi5ctTm+lTfcCW3g==",
       "dev": true
     },
+    "node_modules/mathjs": {
+      "version": "11.5.0",
+      "resolved": "https://registry.npmjs.org/mathjs/-/mathjs-11.5.0.tgz",
+      "integrity": "sha512-vJ/+SqWtxjW6/aeDRt8xL3TlOVKqwN15BIyTGVqGbIWuiqgY4SxZ0yLuna82YH9CB757iFP7uJ4m3KvVBX7Qcg==",
+      "dependencies": {
+        "@babel/runtime": "^7.20.6",
+        "complex.js": "^2.1.1",
+        "decimal.js": "^10.4.3",
+        "escape-latex": "^1.2.0",
+        "fraction.js": "^4.2.0",
+        "javascript-natural-sort": "^0.7.1",
+        "seedrandom": "^3.0.5",
+        "tiny-emitter": "^2.1.0",
+        "typed-function": "^4.1.0"
+      },
+      "bin": {
+        "mathjs": "bin/cli.js"
+      },
+      "engines": {
+        "node": ">= 14"
+      }
+    },
     "node_modules/merge-stream": {
       "version": "2.0.0",
       "resolved": "https://registry.npmjs.org/merge-stream/-/merge-stream-2.0.0.tgz",
@@ -4222,9 +4266,9 @@
       "integrity": "sha512-Gd2UZBJDkXlY7GbJxfsE8/nvKkUEU1G38c1siN6QP6a9PT9MmHB8GnpscSmMJSoF8LOIrt8ud/wPtojys4G6+g=="
     },
     "node_modules/regenerator-runtime": {
-      "version": "0.13.10",
-      "resolved": "https://registry.npmjs.org/regenerator-runtime/-/regenerator-runtime-0.13.10.tgz",
-      "integrity": "sha512-KepLsg4dU12hryUO7bp/axHAKvwGOCV0sGloQtpagJ12ai+ojVDqkeGSiRX1zlq+kjIMZ1t7gpze+26QqtdGqw=="
+      "version": "0.13.11",
+      "resolved": "https://registry.npmjs.org/regenerator-runtime/-/regenerator-runtime-0.13.11.tgz",
+      "integrity": "sha512-kY1AZVr2Ra+t+piVaJ4gxaFaReZVH40AKNo7UCX6W+dEwBo/2oZJzqfuN1qLq1oL45o56cPaTXELwrTh8Fpggg=="
     },
     "node_modules/regexpp": {
       "version": "3.2.0",
@@ -4416,6 +4460,11 @@
         "xen-dev-utils": "github:xenharmonic-devs/xen-dev-utils#v0.1.1"
       }
     },
+    "node_modules/seedrandom": {
+      "version": "3.0.5",
+      "resolved": "https://registry.npmjs.org/seedrandom/-/seedrandom-3.0.5.tgz",
+      "integrity": "sha512-8OwmbklUNzwezjGInmZ+2clQmExQPvomqjL7LFqOYqtmuxRgQYqOD3mHaU+MvZn5FLUeVxVfQjwLZW/n/JFuqg=="
+    },
     "node_modules/semver": {
       "version": "7.3.8",
       "resolved": "https://registry.npmjs.org/semver/-/semver-7.3.8.tgz",
@@ -4770,6 +4819,11 @@
       "integrity": "sha512-w89qg7PI8wAdvX60bMDP+bFoD5Dvhm9oLheFp5O4a2QF0cSBGsBX4qZmadPMvVqlLJBBci+WqGGOAPvcDeNSVg==",
       "dev": true
     },
+    "node_modules/tiny-emitter": {
+      "version": "2.1.0",
+      "resolved": "https://registry.npmjs.org/tiny-emitter/-/tiny-emitter-2.1.0.tgz",
+      "integrity": "sha512-NB6Dk1A9xgQPMoGqC5CVXn123gWyte215ONT5Pp5a0yt4nlEoO1ZWeCwpncaekPHXO60i47ihFnZPiRPjRMq4Q=="
+    },
     "node_modules/tinypool": {
       "version": "0.1.3",
       "resolved": "https://registry.npmjs.org/tinypool/-/tinypool-0.1.3.tgz",
@@ -4920,6 +4974,14 @@
         "url": "https://github.com/sponsors/sindresorhus"
       }
     },
+    "node_modules/typed-function": {
+      "version": "4.1.0",
+      "resolved": "https://registry.npmjs.org/typed-function/-/typed-function-4.1.0.tgz",
+      "integrity": "sha512-DGwUl6cioBW5gw2L+6SMupGwH/kZOqivy17E4nsh1JI9fKF87orMmlQx3KISQPmg3sfnOUGlwVkroosvgddrlg==",
+      "engines": {
+        "node": ">= 14"
+      }
+    },
     "node_modules/typescript": {
       "version": "4.6.4",
       "resolved": "https://registry.npmjs.org/typescript/-/typescript-4.6.4.tgz",
@@ -5397,11 +5459,11 @@
       "integrity": "sha512-qpVT7gtuOLjWeDTKLkJ6sryqLliBaFpAtGeqw5cs5giLldvh+Ch0plqnUMKoVAUS6ZEueQQiZV+p5pxtPitEsA=="
     },
     "@babel/runtime": {
-      "version": "7.19.4",
-      "resolved": "https://registry.npmjs.org/@babel/runtime/-/runtime-7.19.4.tgz",
-      "integrity": "sha512-EXpLCrk55f+cYqmHsSR+yD/0gAIMxxA9QK9lnQWzhMCvt+YmoBN7Zx94s++Kv0+unHk39vxNO8t+CMA2WSS3wA==",
+      "version": "7.20.7",
+      "resolved": "https://registry.npmjs.org/@babel/runtime/-/runtime-7.20.7.tgz",
+      "integrity": "sha512-UF0tvkUtxwAgZ5W/KrkHf0Rn0fdnLDU9ScxBrEVNUprE/MzirjK4MJUX1/BVDv00Sv8cljtukVK1aky++X1SjQ==",
       "requires": {
-        "regenerator-runtime": "^0.13.4"
+        "regenerator-runtime": "^0.13.11"
       }
     },
     "@colors/colors": {
@@ -6388,6 +6450,11 @@
       "integrity": "sha512-gk/Z852D2Wtb//0I+kRFNKKE9dIIVirjoqPoA1wJU+XePVXZfGeBpk45+A1rKO4Q43prqWBNY/MiIeRLbPWUaA==",
       "dev": true
     },
+    "complex.js": {
+      "version": "2.1.1",
+      "resolved": "https://registry.npmjs.org/complex.js/-/complex.js-2.1.1.tgz",
+      "integrity": "sha512-8njCHOTtFFLtegk6zQo0kkVX1rngygb/KQI6z1qZxlFI3scluC+LVTCFbrkWjBv4vvLlbQ9t88IPMC6k95VTTg=="
+    },
     "concat-map": {
       "version": "0.0.1",
       "resolved": "https://registry.npmjs.org/concat-map/-/concat-map-0.0.1.tgz",
@@ -6550,10 +6617,9 @@
       }
     },
     "decimal.js": {
-      "version": "10.4.2",
-      "resolved": "https://registry.npmjs.org/decimal.js/-/decimal.js-10.4.2.tgz",
-      "integrity": "sha512-ic1yEvwT6GuvaYwBLLY6/aFFgjZdySKTE8en/fkU3QICTmRtgtSlFn0u0BXN06InZwtfCelR7j8LRiDI/02iGA==",
-      "dev": true
+      "version": "10.4.3",
+      "resolved": "https://registry.npmjs.org/decimal.js/-/decimal.js-10.4.3.tgz",
+      "integrity": "sha512-VBBaLc1MgL5XpzgIP7ny5Z6Nx3UrRkIViUkPUdtl9aya5amy3De1gsUUSB1g3+3sExYNjCAsAznmukyxCb1GRA=="
     },
     "deep-eql": {
       "version": "3.0.1",
@@ -6820,6 +6886,11 @@
       "dev": true,
       "optional": true
     },
+    "escape-latex": {
+      "version": "1.2.0",
+      "resolved": "https://registry.npmjs.org/escape-latex/-/escape-latex-1.2.0.tgz",
+      "integrity": "sha512-nV5aVWW1K0wEiUIEdZ4erkGGH8mDxGyxSeqPzRNtWP7ataw+/olFObw7hujFWlVjNsaDFw5VZ5NzVSIqRgfTiw=="
+    },
     "escape-string-regexp": {
       "version": "4.0.0",
       "resolved": "https://registry.npmjs.org/escape-string-regexp/-/escape-string-regexp-4.0.0.tgz",
@@ -7707,6 +7778,11 @@
       "integrity": "sha512-Yljz7ffyPbrLpLngrMtZ7NduUgVvi6wG9RJ9IUcyCd59YQ911PBJphODUcbOVbqYfxe1wuYf/LJ8PauMRwsM/g==",
       "dev": true
     },
+    "javascript-natural-sort": {
+      "version": "0.7.1",
+      "resolved": "https://registry.npmjs.org/javascript-natural-sort/-/javascript-natural-sort-0.7.1.tgz",
+      "integrity": "sha512-nO6jcEfZWQXDhOiBtG2KvKyEptz7RVbpGP4vTD2hLBdmNQSsCiicO2Ioinv6UI4y9ukqnBpy+XZ9H6uLNgJTlw=="
+    },
     "jazz-midi": {
       "version": "1.7.6",
       "resolved": "https://registry.npmjs.org/jazz-midi/-/jazz-midi-1.7.6.tgz",
@@ -8031,6 +8107,22 @@
       "integrity": "sha512-CkYQrPYZfWnu/DAmVCpTSX/xHpKZ80eKh2lAkyA6AJTef6bW+6JpbQZN5rofum7da+SyN1bi5ctTm+lTfcCW3g==",
       "dev": true
     },
+    "mathjs": {
+      "version": "11.5.0",
+      "resolved": "https://registry.npmjs.org/mathjs/-/mathjs-11.5.0.tgz",
+      "integrity": "sha512-vJ/+SqWtxjW6/aeDRt8xL3TlOVKqwN15BIyTGVqGbIWuiqgY4SxZ0yLuna82YH9CB757iFP7uJ4m3KvVBX7Qcg==",
+      "requires": {
+        "@babel/runtime": "^7.20.6",
+        "complex.js": "^2.1.1",
+        "decimal.js": "^10.4.3",
+        "escape-latex": "^1.2.0",
+        "fraction.js": "^4.2.0",
+        "javascript-natural-sort": "^0.7.1",
+        "seedrandom": "^3.0.5",
+        "tiny-emitter": "^2.1.0",
+        "typed-function": "^4.1.0"
+      }
+    },
     "merge-stream": {
       "version": "2.0.0",
       "resolved": "https://registry.npmjs.org/merge-stream/-/merge-stream-2.0.0.tgz",
@@ -8432,9 +8524,9 @@
       }
     },
     "regenerator-runtime": {
-      "version": "0.13.10",
-      "resolved": "https://registry.npmjs.org/regenerator-runtime/-/regenerator-runtime-0.13.10.tgz",
-      "integrity": "sha512-KepLsg4dU12hryUO7bp/axHAKvwGOCV0sGloQtpagJ12ai+ojVDqkeGSiRX1zlq+kjIMZ1t7gpze+26QqtdGqw=="
+      "version": "0.13.11",
+      "resolved": "https://registry.npmjs.org/regenerator-runtime/-/regenerator-runtime-0.13.11.tgz",
+      "integrity": "sha512-kY1AZVr2Ra+t+piVaJ4gxaFaReZVH40AKNo7UCX6W+dEwBo/2oZJzqfuN1qLq1oL45o56cPaTXELwrTh8Fpggg=="
     },
     "regexpp": {
       "version": "3.2.0",
@@ -8560,6 +8652,11 @@
         "xen-dev-utils": "github:xenharmonic-devs/xen-dev-utils#v0.1.1"
       }
     },
+    "seedrandom": {
+      "version": "3.0.5",
+      "resolved": "https://registry.npmjs.org/seedrandom/-/seedrandom-3.0.5.tgz",
+      "integrity": "sha512-8OwmbklUNzwezjGInmZ+2clQmExQPvomqjL7LFqOYqtmuxRgQYqOD3mHaU+MvZn5FLUeVxVfQjwLZW/n/JFuqg=="
+    },
     "semver": {
       "version": "7.3.8",
       "resolved": "https://registry.npmjs.org/semver/-/semver-7.3.8.tgz",
@@ -8821,6 +8918,11 @@
       "integrity": "sha512-w89qg7PI8wAdvX60bMDP+bFoD5Dvhm9oLheFp5O4a2QF0cSBGsBX4qZmadPMvVqlLJBBci+WqGGOAPvcDeNSVg==",
       "dev": true
     },
+    "tiny-emitter": {
+      "version": "2.1.0",
+      "resolved": "https://registry.npmjs.org/tiny-emitter/-/tiny-emitter-2.1.0.tgz",
+      "integrity": "sha512-NB6Dk1A9xgQPMoGqC5CVXn123gWyte215ONT5Pp5a0yt4nlEoO1ZWeCwpncaekPHXO60i47ihFnZPiRPjRMq4Q=="
+    },
     "tinypool": {
       "version": "0.1.3",
       "resolved": "https://registry.npmjs.org/tinypool/-/tinypool-0.1.3.tgz",
@@ -8934,6 +9036,11 @@
       "integrity": "sha512-Ne+eE4r0/iWnpAxD852z3A+N0Bt5RN//NjJwRd2VFHEmrywxf5vsZlh4R6lixl6B+wz/8d+maTSAkN1FIkI3LQ==",
       "dev": true
     },
+    "typed-function": {
+      "version": "4.1.0",
+      "resolved": "https://registry.npmjs.org/typed-function/-/typed-function-4.1.0.tgz",
+      "integrity": "sha512-DGwUl6cioBW5gw2L+6SMupGwH/kZOqivy17E4nsh1JI9fKF87orMmlQx3KISQPmg3sfnOUGlwVkroosvgddrlg=="
+    },
     "typescript": {
       "version": "4.6.4",
       "resolved": "https://registry.npmjs.org/typescript/-/typescript-4.6.4.tgz",
diff --git a/package.json b/package.json
index f4f602de..dd738e45 100644
--- a/package.json
+++ b/package.json
@@ -14,14 +14,15 @@
   },
   "dependencies": {
     "jszip": "^3.10.1",
+    "mathjs": "^11.5.0",
     "moment-of-symmetry": "github:xenharmonic-devs/moment-of-symmetry#v0.2.1",
     "qs": "^6.11.0",
+    "scale-workshop-core": "github:xenharmonic-devs/scale-workshop-core#v0.0.1",
     "temperaments": "github:xenharmonic-devs/temperaments#v0.3.0",
     "vue": "^3.2.33",
     "vue-router": "^4.1.5",
     "webmidi": "^3.0.21",
-    "xen-dev-utils": "github:xenharmonic-devs/xen-dev-utils#v0.1.0",
-    "scale-workshop-core": "github:xenharmonic-devs/scale-workshop-core#v0.0.1"
+    "xen-dev-utils": "github:xenharmonic-devs/xen-dev-utils#v0.1.0"
   },
   "devDependencies": {
     "@rushstack/eslint-patch": "^1.2.0",
diff --git a/src/__tests__/tempering.spec.ts b/src/__tests__/tempering.spec.ts
index 9e600a0f..d82b220d 100644
--- a/src/__tests__/tempering.spec.ts
+++ b/src/__tests__/tempering.spec.ts
@@ -7,9 +7,125 @@ import {
   makeRank2FromVals,
   mosPatternsRank2FromCommas,
   mosPatternsRank2FromVals,
+  vanishCommas,
+  tenneyVals,
+  toPrimeMapping,
 } from "../tempering";
-import { arraysEqual, Fraction, valueToCents } from "xen-dev-utils";
+import {
+  arraysEqual,
+  dot,
+  Fraction,
+  PRIMES,
+  PRIME_CENTS,
+  toMonzoAndResidual,
+  valueToCents,
+} from "xen-dev-utils";
 import { ExtendedMonzo, Interval, Scale } from "scale-workshop-core";
+import { Subgroup } from "temperaments";
+import { DEFAULT_NUMBER_OF_COMPONENTS } from "../constants";
+
+describe("Comma vanisher", () => {
+  it("can make the syntonic comma disappear (tempered octaves)", () => {
+    const inital = PRIME_CENTS.slice(0, 3);
+    const syntonic = [-4, 4, -1];
+    const mapping = vanishCommas(inital, [syntonic]);
+    expect(dot(mapping, syntonic)).toBeCloseTo(0);
+
+    const octave = mapping[0];
+    expect(octave).not.toBe(1200);
+    expect(octave).toBeLessThan(1202);
+    expect(octave).toBeGreaterThan(1198);
+  });
+
+  it("can make the syntonic comma disappear (tempered octaves with weights)", () => {
+    const inital = PRIME_CENTS.slice(0, 3);
+    const syntonic = [-4, 4, -1];
+    const mapping = vanishCommas(inital, [syntonic], [100, 3, 2]);
+    expect(dot(mapping, syntonic)).toBeCloseTo(0);
+
+    const octave = mapping[0];
+    expect(octave).not.toBe(1200);
+    expect(octave).toBeLessThan(1201);
+    expect(octave).toBeGreaterThan(1199);
+  });
+
+  it("can make the syntonic comma disappear (pure octaves)", () => {
+    const inital = PRIME_CENTS.slice(0, 3);
+    const syntonic = [-4, 4, -1];
+    const mapping = vanishCommas(inital, [syntonic], undefined, false);
+    expect(dot(mapping, syntonic)).toBeCloseTo(0);
+
+    const octave = mapping[0];
+    expect(octave).toBe(1200);
+
+    const twelfth = mapping[1];
+    expect(twelfth).not.toBe(PRIME_CENTS[1]);
+    expect(twelfth).toBeLessThan(1905);
+    expect(twelfth).toBeGreaterThan(1896);
+
+    const five = mapping[2];
+    expect(five).not.toBe(PRIME_CENTS[2]);
+    expect(five).toBeLessThan(2789);
+    expect(five).toBeGreaterThan(2783);
+  });
+
+  it("can handle big subgroups (ratio units)", () => {
+    const initial = PRIMES.slice(0, 25);
+    const commas = [
+      toMonzoAndResidual(new Fraction(621, 620), 25)[0],
+      toMonzoAndResidual(new Fraction(87, 86), 25)[0],
+      toMonzoAndResidual(new Fraction(98, 97), 25)[0],
+    ];
+    const mapping = vanishCommas(initial, commas, undefined, false, "ratio");
+
+    for (const comma of commas) {
+      let interval = 1;
+      for (let i = 0; i < 25; ++i) {
+        interval *= mapping[i] ** comma[i];
+      }
+      expect(interval).toBeCloseTo(1);
+    }
+  });
+});
+
+describe("Tenney-Euclid optimal val combiner", () => {
+  it("calculates POTE meantone", () => {
+    const jip = PRIME_CENTS.slice(0, 3);
+    const twelve = [12, 19, 28];
+    const nineteen = [19, 30, 44];
+
+    const mapping = tenneyVals(jip, [twelve, nineteen]);
+
+    const syntonic = [-4, 4, -1];
+    expect(dot(mapping, syntonic)).toBeCloseTo(0);
+
+    const pote = mapping.map((m) => (1200 * m) / mapping[0]);
+    expect(dot(pote, [-1, 1, 0])).toBeCloseTo(696.239);
+  });
+});
+
+describe("Prime map converter", () => {
+  it("does (almost) nothing in 5-limit JI", () => {
+    const fiveLimit = PRIME_CENTS.slice(0, 3);
+    const mapping = toPrimeMapping(fiveLimit, new Subgroup(5));
+    expect(mapping[0]).toBe(fiveLimit[0]);
+    expect(mapping[1]).toBe(fiveLimit[1]);
+    expect(mapping[2]).toBe(fiveLimit[2]);
+    expect(mapping.length).toBe(DEFAULT_NUMBER_OF_COMPONENTS);
+    expect(mapping[3]).toBe(PRIME_CENTS[3]);
+  });
+
+  it("converts a mapping in 2.3.13/5 to 2.3.5.7.11.13...", () => {
+    const original = [1200, 1901, 1654];
+    const mapping = toPrimeMapping(original, new Subgroup("2.3.13/5"));
+    expect(mapping[0]).toBeCloseTo(1200);
+    expect(mapping[1]).toBeCloseTo(1901);
+    expect(mapping[3]).toBeCloseTo(PRIME_CENTS[3]);
+    expect(mapping[4]).toBeCloseTo(PRIME_CENTS[4]);
+    expect(mapping[5] - mapping[2]).toBeCloseTo(1654);
+    expect(mapping[6]).toBeCloseTo(PRIME_CENTS[6]);
+  });
+});
 
 describe("Temperament Mapping", () => {
   it("calculates POTE meantone", () => {
diff --git a/src/components/modals/generation/RankTwo.vue b/src/components/modals/generation/RankTwo.vue
index 1e0b36a4..0058e97f 100644
--- a/src/components/modals/generation/RankTwo.vue
+++ b/src/components/modals/generation/RankTwo.vue
@@ -1,5 +1,8 @@
 <script setup lang="ts">
-import { DEFAULT_NUMBER_OF_COMPONENTS } from "@/constants";
+import {
+  DEFAULT_NUMBER_OF_COMPONENTS,
+  MAX_INTERACTIVE_SUBGROUP_SIZE,
+} from "@/constants";
 import {
   makeRank2FromVals,
   makeRank2FromCommas,
@@ -100,7 +103,7 @@ const [mosPatterns, mosPatternsError] = computedAndError(() => {
       return [];
     }
     // Huge subgroups get too expensive to evaluate interactively
-    if (subgroup.value.basis.length > 6) {
+    if (subgroup.value.basis.length > MAX_INTERACTIVE_SUBGROUP_SIZE) {
       return expensiveMosPatterns.value;
     }
     return mosPatternsRank2FromVals(
@@ -116,7 +119,7 @@ const [mosPatterns, mosPatternsError] = computedAndError(() => {
       return [];
     }
     // Huge subgroups get too expensive to evaluate interactively
-    if (subgroup.value.basis.length > 6) {
+    if (subgroup.value.basis.length > MAX_INTERACTIVE_SUBGROUP_SIZE) {
       return expensiveMosPatterns.value;
     }
     return mosPatternsRank2FromCommas(
diff --git a/src/components/modals/modification/TemperScale.vue b/src/components/modals/modification/TemperScale.vue
index 4eaede80..1fa5a9db 100644
--- a/src/components/modals/modification/TemperScale.vue
+++ b/src/components/modals/modification/TemperScale.vue
@@ -1,10 +1,13 @@
 <script setup lang="ts">
-import { DEFAULT_NUMBER_OF_COMPONENTS } from "@/constants";
-import { Mapping } from "@/tempering";
-import { ref, watch } from "vue";
+import {
+  DEFAULT_NUMBER_OF_COMPONENTS,
+  MAX_GEO_SUBGROUP_SIZE,
+} from "@/constants";
+import { Mapping, tenneyVals, toPrimeMapping, vanishCommas } from "@/tempering";
+import { computed, ref, watch } from "vue";
 import Modal from "@/components/ModalDialog.vue";
 import { makeState, splitText } from "@/components/modals/tempering-state";
-import { PRIME_CENTS } from "xen-dev-utils";
+import { natsToCents, PRIME_CENTS } from "xen-dev-utils";
 import type { Scale } from "scale-workshop-core";
 
 const props = defineProps<{
@@ -40,6 +43,10 @@ const commas = state.commas;
 const subgroup = state.subgroup;
 const options = state.options;
 
+const constraintsDisabled = computed(
+  () => subgroup.value.basis.length > MAX_GEO_SUBGROUP_SIZE
+);
+
 watch(subgroupError, (newValue) =>
   subgroupInput.value!.setCustomValidity(newValue)
 );
@@ -58,19 +65,60 @@ function modify() {
       }
       mapping = new Mapping(vector.slice(0, DEFAULT_NUMBER_OF_COMPONENTS));
     } else if (method.value === "vals") {
-      mapping = Mapping.fromVals(
-        vals.value,
-        DEFAULT_NUMBER_OF_COMPONENTS,
-        subgroup.value,
-        options.value
-      );
+      if (constraintsDisabled.value) {
+        // Subgroup is too large to use geometric methods. Use O(n²) projection instead.
+        const weights = options.value.weights;
+        // True constraints are not supported so CTE is interpreted as POTE.
+        const temperEquaves =
+          options.value.temperEquaves && tempering.value !== "CTE";
+
+        const jip = subgroup.value.jip().map(natsToCents);
+        const valVectors = vals.value.map((val) =>
+          subgroup.value.fromWarts(val)
+        );
+        let mappingVector = tenneyVals(jip, valVectors, weights);
+        if (!temperEquaves) {
+          mappingVector = mappingVector.map(
+            (m) => (jip[0] * m) / mappingVector[0]
+          );
+        }
+        mapping = new Mapping(toPrimeMapping(mappingVector, subgroup.value));
+      } else {
+        mapping = Mapping.fromVals(
+          vals.value,
+          DEFAULT_NUMBER_OF_COMPONENTS,
+          subgroup.value,
+          options.value
+        );
+      }
     } else {
-      mapping = Mapping.fromCommas(
-        commas.value,
-        DEFAULT_NUMBER_OF_COMPONENTS,
-        subgroup.value,
-        options.value
-      );
+      if (constraintsDisabled.value) {
+        // Subgroup is too large to use geometric methods. Use O(n) gradient descent instead.
+        // True constraints are not supported so CTE is interpreted as pure equaves.
+        const temperEquaves =
+          options.value.temperEquaves && tempering.value !== "CTE";
+        const weights = options.value.weights;
+
+        const jip = subgroup.value.jip().map(natsToCents);
+        const commaMonzos = commas.value.map(
+          (comma) => subgroup.value.toMonzoAndResidual(comma)[0]
+        );
+
+        const mappingVector = vanishCommas(
+          jip,
+          commaMonzos,
+          weights,
+          temperEquaves
+        );
+        mapping = new Mapping(toPrimeMapping(mappingVector, subgroup.value));
+      } else {
+        mapping = Mapping.fromCommas(
+          commas.value,
+          DEFAULT_NUMBER_OF_COMPONENTS,
+          subgroup.value,
+          options.value
+        );
+      }
     }
     emit(
       "update:scale",
@@ -214,6 +262,7 @@ function modify() {
                 id="tempering-CTE"
                 value="CTE"
                 @focus="error = ''"
+                :disabled="constraintsDisabled"
                 v-model="tempering"
               />
               <label for="tempering-CTE"> CTE </label>
@@ -225,6 +274,7 @@ function modify() {
             <textarea
               id="constraints"
               @focus="error = ''"
+              :disabled="constraintsDisabled"
               v-model="constraintsString"
             ></textarea>
           </div>
diff --git a/src/constants.ts b/src/constants.ts
index 9e1ce571..773af799 100644
--- a/src/constants.ts
+++ b/src/constants.ts
@@ -25,3 +25,10 @@ export const KORG = {
 
 // Browser interaction
 export const LEFT_MOUSE_BTN = 0;
+
+// Sanity limits for tempering
+
+// Anything larger than this isn't evaluated interactively
+export const MAX_INTERACTIVE_SUBGROUP_SIZE = 6;
+// Anything larger than this uses O(n²) methods (if available) instead of O(exp(n))
+export const MAX_GEO_SUBGROUP_SIZE = 9;
diff --git a/src/tempering.ts b/src/tempering.ts
index 96a6ac3a..31a867cd 100644
--- a/src/tempering.ts
+++ b/src/tempering.ts
@@ -8,16 +8,180 @@ import {
   type Weights,
   Subgroup,
   type JipOrLimit,
+  type Comma,
+  type PitchUnits,
 } from "temperaments";
 import { DEFAULT_NUMBER_OF_COMPONENTS } from "./constants";
 import {
+  centsToNats,
+  dot,
+  natsToCents,
+  natsToSemitones,
   PRIME_CENTS,
+  semitonesToNats,
+  toMonzo,
   valueToCents,
   type FractionValue,
   type Monzo,
 } from "xen-dev-utils";
 import { Interval, Scale } from "scale-workshop-core";
 
+import { pinv, multiply, lusolve } from "mathjs";
+
+/**
+ * Find a Tenney-Euclid optimal linear combination of vals.
+ * @param jip Just intonation point (JIP).
+ * @param vals Array of vals in using the JIP's semantics.
+ * @param weights Importance weighting for the JIP's coordinates (defaults to 1 / JIP).
+ * @param units The units pitch of intervals and mappings are measured in.
+ * @returns A Tenney-Euclid optimal mapping representing a temperament supported by all of the vals.
+ */
+export function tenneyVals(
+  jip: number[],
+  vals: Val[],
+  weights?: Weights,
+  units: PitchUnits = "cents"
+) {
+  if (units === "cents") {
+    jip = jip.map(centsToNats);
+  } else if (units === "semitones") {
+    jip = jip.map(semitonesToNats);
+  } else if (units === "ratio") {
+    jip = jip.map(Math.log);
+  }
+
+  if (weights === undefined) {
+    weights = jip.map((j) => 1 / j);
+  }
+
+  vals = vals.map((val) => val.map((v, i) => v * weights![i]));
+  jip = jip.map((j, i) => j * weights![i]);
+
+  const mapping = multiply(jip, multiply(pinv(vals), vals)).map(
+    (m, i) => m / weights![i]
+  );
+
+  if (units === "cents") {
+    return mapping.map(natsToCents);
+  } else if (units === "semitones") {
+    return mapping.map(natsToSemitones);
+  } else if (units === "ratio") {
+    return mapping.map(Math.exp);
+  }
+  return mapping;
+}
+
+function norm(monzo: Monzo) {
+  let total = 0;
+  monzo.forEach((component) => {
+    total += component * component;
+  });
+  return Math.sqrt(total);
+}
+
+function scalarMul(scalar: number, monzo: Monzo) {
+  return monzo.map((component) => scalar * component);
+}
+
+function subInPlace(a: Monzo, b: Monzo) {
+  for (let i = 0; i < a.length; ++i) {
+    a[i] -= b[i];
+  }
+}
+
+/**
+ * Adjust mapping until specified commas vanish.
+ * @param jip Just intonation point (JIP).
+ * @param commas Array of commas in the mapping's semantics.
+ * @param weights Importance weighting for the JIP's coordinates (defaults to 1 / JIP).
+ * @param temperEquaves If `true` tempering is applied to octaves as well.
+ * @param units The units pitch of intervals and mappings are measured in.
+ * @param numberOfIterations Number of iterations to adjust the mapping.
+ * @returns A close-by mapping where the commas vanish.
+ */
+export function vanishCommas(
+  jip: number[],
+  commas: Comma[],
+  weights?: Weights,
+  temperEquaves = true,
+  units: PitchUnits = "cents",
+  numberOfIterations = 1000
+) {
+  // The process is linear and scale-free in log-space so the particular units don't matter.
+  if (units === "ratio") {
+    jip = jip.map(Math.log);
+  }
+
+  if (weights === undefined) {
+    weights = jip.map((j) => 1 / j);
+  }
+  weights = weights.map((w) => w / weights![0]);
+
+  let mapping = jip.slice().map((j, i) => j * weights![i]);
+
+  const normalizedCommas = commas
+    .map((comma) => comma.map((c, i) => c / weights![i]))
+    .map((comma) => scalarMul(1 / norm(comma), comma));
+
+  for (let i = 0; i < numberOfIterations; ++i) {
+    for (const comma of normalizedCommas) {
+      const delta = scalarMul(dot(mapping, comma), comma);
+      if (!temperEquaves) {
+        delta[0] = 0;
+      }
+      subInPlace(mapping, delta);
+    }
+  }
+
+  mapping = mapping.map((m, i) => m / weights![i]);
+
+  if (units === "ratio") {
+    return mapping.map(Math.exp);
+  }
+  return mapping;
+}
+
+export function toPrimeMapping(mapping: number[], subgroup: Subgroup) {
+  // Code copied from temperaments package and converted to cents + using mathjs lin solver
+
+  const basisMonzos = subgroup.basis.map((b) => toMonzo(b));
+  const limit = basisMonzos.reduce((a, b) => Math.max(a, b.length), 0);
+
+  // Calculate the full matrix and solve BasisMatrix * result = mapping
+  const missing = new Set<number>();
+  for (let i = 0; i < limit; ++i) {
+    missing.add(i);
+  }
+  basisMonzos.forEach((monzo) => {
+    monzo.forEach((component, j) => {
+      if (component > 0) {
+        missing.delete(j);
+      }
+    });
+    while (monzo.length < limit) {
+      monzo.push(0);
+    }
+  });
+  for (const index of missing) {
+    const extraBasis = Array(limit).fill(0);
+    extraBasis[index] = 1;
+    basisMonzos.push(extraBasis);
+  }
+  const mapping_ = [...mapping];
+  while (mapping_.length < limit) {
+    mapping_.push(dot(basisMonzos[mapping_.length], PRIME_CENTS));
+  }
+  const result = lusolve(basisMonzos, mapping_).flat();
+
+  while (result.length > DEFAULT_NUMBER_OF_COMPONENTS) {
+    result.pop();
+  }
+  while (result.length < DEFAULT_NUMBER_OF_COMPONENTS) {
+    result.push(PRIME_CENTS[result.length]);
+  }
+  return result as number[];
+}
+
 export class Mapping {
   vector: number[];