unequaltemperament

Emotional Mapping Project Documents

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How Tuning Systems Paint Emotion

Each musical key's emotional color is shaped by how fast its intervals beat—specifically the major third. A major third that is wide of just intonation beats faster; one that is close to just beats slowly or not at all. Fast-beating thirds feel agitated, tense, and energized. Slow-beating thirds feel calm, warm, and intimate. The central question of this project is: can a tuning system paint different emotional states in different keys?

Equal Temperament — emotionally monochrome All 24 major thirds are exactly 13.69 cents wide—identical beating in every key. No key feels different from any other. A composer cannot choose C major for serenity and C‑sharp major for agitation: the tuning makes them acoustically interchangeable.
Well Temperaments — a palette of character Systems like Vallotti or Werckmeister III distribute the syntonic comma unevenly. Some keys receive narrow thirds (calm, luminous) while others receive wider thirds (energized, tense). Composers can genuinely select keys for their emotional character.
Meantone Temperaments — bimodal extremes Standard 1/4-comma meantone gives eight near-pure thirds (serenely beating) and four "wolf" thirds (harshly beating). There is almost nothing in between. This covers only two emotional zones—pure calm and intense agitation—missing the rich middle range of grief, hope, wonder, and pride.
Range width = emotional reach A tuning system's capacity to portray diverse emotions can be summarized by how many distinct beat-speed zones it can place across its twelve keys. A system covering zones 1–4 can express states from serene contentment through spirited exultation; one stuck in zone 3 alone cannot distinguish emotions at all.

The 24 Emotional States

Source: Emotion Taxonomy (deep-research-report2.md) · Cross-referenced with 24 Musical Key Profiles. Arousal badges: High Med Low

E01–E12  ·  Luminous states — positive and approach-oriented

E01 Ruby Exultation Joy · delight · elation High
E02 Honeyed Merriment Amusement · mirth · cheer High
E03 Jasmine Contentment Serenity · ease · calm pleasure Low
E04 Peppermint Relief Reprieve · release · decompression Med
E05 Rose Quartz Devotion Love · tenderness · trust Med
E06 Emerald Gratitude Appreciation · warmth · elevation Med
E07 Saffron Inquiry Curiosity · fascination · interest High
E08 Cardamom Hope Optimism · determination Med
E09 Opal Wonder Awe · reverence · amazement Med
E10 Star Anise Startle Surprise · shock · astonishment High
E11 Sunstone Sovereignty Pride · accomplishment · self-respect Med
E12 Sapphire Self-Efficacy Confidence · competence · steadiness Med

E13–E24  ·  Shadow states — negative and avoidance-oriented

E13 Cayenne Indignation Anger · irritation · outrage High
E14 Vinegar Resentment Bitterness · grievance · hostility Med
E15 Obsidian Alarm Fear · anxiety · dread High
E16 Nightshade Panic Terror · overwhelm · acute dread High
E17 Bluebell Grief Sadness · sorrow · loneliness Low
E18 Lavender Melancholy Wistfulness · nostalgia · pensiveness Low
E19 Wormwood Aversion Disgust · distaste · recoil Med
E20 Black Salt Contempt Disdain · scorn · moral condemnation Med
E21 Virgo Blush Shame · humiliation · exposure Med
E22 Chicory Guilt Remorse · regret · moral concern Med
E23 Slate Stillness Apathy · blunting · indifference Low
E24 Barley Boredom Restlessness · listlessness · tedium Med
Zone 1 Serene (< 2¢) — E03 E23 Zone 2 Tender (2–8¢) — E17 E18 E04 E05 Zone 3 Centered (8–14¢) — E06 E08 E09 E14 Zone 4 Spirited (14–20¢) — E02 E07 E11 E12 Zone 5 Agitated (≥ 20¢) — E01 E13 E15 E16

Temperament Emotional Range

For each of ten representative tuning systems, the table below shows how many of the twelve major keys fall into each M3 beat-speed zone. A system that covers more zones can express a wider range of emotional states through key choice alone. M3 dev = how many cents the major third exceeds just intonation (386.31¢); ET = 13.69¢. Computed from api_export_temperaments_20260227.json.

Tuning System M3 dev
range		 Zone 1
Serene
< 2¢ 		Zone 2
Tender
2–8¢ 		Zone 3
Centered
8–14¢ 		Zone 4
Spirited
14–20¢ 		Zone 5
Agitated
≥ 20¢ 		Zones
covered		 Emotional reach
E03 E23 E17 E18 E04 E05 E06 E08 E09 E14 E02 E07 E11 E12 E01 E13 E15 E16
Equal Temperament 12.7–14.7¢ — — 7 5 — 2/5 Narrow
Viennese (Hummel) 12.8–14.6¢ — — 8 4 — 2/5 Narrow
C.P.E. Bach 12.1–16.8¢ — — 7 5 — 2/5 Narrow
Neidhardt Small City 5.9–17.6¢ — 2 4 6 — 3/5 Moderate
Vallotti–Young 5.9–21.5¢ — 3 4 2 3 4/5 Broad
Vallotti 5.9–21.5¢ — 3 4 2 3 4/5 Broad
Werckmeister III 3.9–21.5¢ — 2 3 4 3 4/5 Broad
Kirnberger III 0–21.5¢ 1 2 2 5 2 5/5 Full spectrum
1/6-comma Meantone 7.2–26.7¢ — 8 — — 4 2/5 Narrow
1/4-comma Meantone -0–41.1¢ 8 — — — 4 2/5 Narrow

Note on 1/4-comma Meantone: its bimodal distribution (8 serene keys + 4 agitated wolf thirds, nothing between) means it can only paint two emotional extremes—it actually covers fewer emotional zones than a good well temperament, despite having purer thirds overall.

Dissertation Sketch Chapters

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