Collected Illustrations of the Three Realms, Volume 73

The Fifth Palace: Ablution

Divide by three to get 16,250 / Subtract a third to generate Echoing Bell; used in calculation.
Yu Corresponds to the "Shang" of Great Flourishing Resonating Official Corresponds to the Palace of Mean Pipe Shang Corresponds to the "Yu" of Forest Bell Jue Corresponds to the "Zhi" of Southern Pipe Altered Zhi The "Altered Zhi" (Bianzhi) is a sharpened fourth or a tritone, acting as a passing tone in the scale.

The Sixth Palace: Echoing Bell

Divide by three to get 32,450 / Add a third to generate Luxuriant Guest.
Shang Corresponds to the "Yu" of Great Flourishing Jue Corresponds to the "Zhi" of Ablution Altered Zhi Corresponds to the "Jue" of Forest Bell / When used, the "Yu" serves as "Shang" Resonating Official

The Seventh Palace: Luxuriant Guest

Divide by three to get 43,472 / Add a third to generate Greater Pipe.
Zhi Corresponds to the "Jue" of Great Flourishing Yu Corresponds to the "Shang" of Ablution Resonating Official Corresponds to the "Zhi" of Mean Pipe Altered Shang Corresponds to the "Yu" of Southern Pipe Jue Corresponds to the "Zhi" of Echoing Bell

The Eighth Palace: Greater Pipe

Divide by three to get 55,396 / Subtract a third to generate Equalizer.
Resonating Official Corresponds to the "Shang" of Great Flourishing Shang Corresponds to the "Jue" of Ablution Jue Corresponds to the "Altered Zhi" of Luxuriant Guest Zhi Corresponds to the "Yu" of Southern Pipe Yu Corresponds to the "Shang" of Echoing Bell

The Ninth Palace: Equalizer

Divide by three to get 16,881 / Add a third to generate Pressed Bell.
Jue Corresponds to the "Zhi" of Greater Pipe Altered Zhi Corresponds to the "Yu" of Luxuriant Guest Yu Corresponds to the "Shang" of Southern Pipe Resonating Official Corresponds to the Palace of Pressed Bell Shang Corresponds to the "Yu" of Mean Pipe

The Tenth Palace: Pressed Bell

Divide by three to get 49,152 / Subtract a third to generate Strict Pipe.
Yu Corresponds to the "Shang" of Greater Pipe Resonating Official Corresponds to the "Jue" of Ablution Shang Corresponds to the "Yu" of Luxuriant Guest Jue Corresponds to the "Zhi" of Equalizer Altered Zhi Corresponds to the "Jue" of Southern Pipe

The Eleventh Palace: Strict Pipe

Divide by three to get 33,716 / Add a third to generate Mean Pipe.
Shang Corresponds to the "Yu" of Greater Pipe Jue Corresponds to the "Altered Zhi" of Luxuriant Guest Zhi Corresponds to the "Yu" of Southern Pipe Yu Corresponds to the "Shang" of Echoing Bell Resonating Official Corresponds to the Altered Palace of Echoing Bell

The Twelfth Palace: Mean Pipe

Divide by three to get 46,653 / The 501 generated in the middle are considered "Small". This likely refers to the "comma," a slight mathematical discrepancy that occurs when completing the cycle of pitches.
Zhi Corresponds to the "Jue" of Greater Pipe Yu Corresponds to the "Altered Zhi" of Luxuriant Guest Resonating Official Corresponds to the "Shang" of Equalizer Shang Corresponds to the "Yu" of Southern Pipe Jue Corresponds to the "Zhi" of Strict Pipe Altered Zhi

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According to the "Book of Pitch-Pipes" in the Records of the Grand Historian original: 史記律書, Shiji Lushu—the earliest systematic Chinese text on music theory, these principles are primary. They are the source upon which the "Treatises" of the History of the Later Han original: 後漢志, Houhanshu Zhi were based, and within them, the methods for performing music are resided. Generally, for all measurements...