Na-Yin (纳音), meaning “Received Sounds”, is an ancient Chinese metaphysical system used to correlating the Heavenly Stems (天干) and Earthly Branches (地支) to one of the Five Phases (五行) and specific symbolic Key (音), which is a combination of Tonic (律) and Mode (调)
SEXAGENERY-CYCLE correspondance with 60 MUSICAL-KEYS 納音
Shen Kuo wiki states: the SEXAGENERY-CYCLE have corresponding 60 KEYS wiki, which originates from the principle of the 12 TONICS wiki (based on 12 tones equal temperament wiki) times 5 MODES wiki (based on pentatonic scale wiki). One PITCH contains 5 KEYS, 12 PITCHES contains 60 KEYs.
| # of Semitones wiki | Interval wiki | Short | 12 TET | Just intonation wiki | Pythagorean tuning wiki | 12-PITCHES | 1/3 Loss and Gain |
|---|---|---|---|---|---|---|---|
| 0 | Perfect unison | P1 | 2^(0/12) | 1/1 | 1/1 | T0黄钟P1 | 1/1 |
| 1 | Minor second | m2 | 2^(1/12) | 16/15 | (2/3)^5 * 2^3 | T1大吕m2 | (3/2)^4 * (3/4)^3 |
| 2 | Major second | M2 | 2^(2/12) | 9/8 | (3/2)^2 * 1/2 | T2太簇M2 | 3/2 * 3/4 |
| 3 | Minor third | m3 | 2^(3/12) | 6/5 | (2/3)^3 * 2^2 | T3夹钟m3 | (3/2)^5 * (3/4)^4 |
| 4 | Major third | M3 | 2^(4/12) | 5/4 | (3/2)^4 * (1/2)^2 | T4姑洗M3 | (3/2)^2 * (3/4)^2 |
| 5 | Perfect fourth (F) | P4 | 2^(5/12) | 4/3 | 2/3 * 2 | T5仲吕P4 | (3/2)^6 * (3/4)^5 |
| 6 | Tritone | TT | 2^(6/12) | 64/45 | (2/3)^6 * 2^4 and (3/2)^6 * (1/2)^3 | T6蕤宾TT | (3/2)^3 * (3/4)^3 |
| 7 | Perfect fifth | P5 | 2^(7/12) | 3/2 | 3/2 | T7林钟P5 | 3/2 |
| 8 | Minor sixth | m6 | 2^(8/12) | 8/5 | (2/3)^4 * 2^3 | T8夷则m6 | (3/2)^4 * (3/4)^4 |
| 9 | Major sixth | M6 | 2^(9/12) | 5/3 | (3/2)^3 * 1/2 | T9南吕M6 | (3/2)^2 * 3/4 |
| 10 | Minor seventh | m7 | 2^(10/12) | 16/9 | (2/3)^2 * 2^2 | TA无射m7 | (3/2)^5 * (3/4)^5 |
| 11 | Major seventh | M7 | 2^(11/12) | 15/8 | (3/2)^5 * (1/2)^2 | TB应钟M7 | (3/2)^3 * (3/4)^2 |
| 12 | Perfect octave | P8 | 2^(12/12) | 2/1 | 2/1 | T0黄钟P8 | (3/2)^6 * (3/4)^6 |
| Mode | Sequence of Intervals | Relative to Major scale | # of Semitones from Tonic for 1st-2nd-3rd-4th-5th degree wiki | Example with Tonic T0黄钟 |
|---|---|---|---|---|
| DO宫EARTH | W-W-3/2-W-3/2 | DO宫-RE商-MI角-SO徵-LA羽 | 0-2-4-7-9 | T0黄钟P1-T2太簇M2-T4姑洗M3-T7林钟P5-T9南吕M6 |
| RE商METAL | W-3/2-W-3/2-W | DO宫-RE商-MI♯清角-SO徵-LA♯清羽 | 0-2-5-7-10 | T0黄钟P1-T2太簇M2-T5仲吕P4-T7林钟P5-TA无射m7 |
| MI角WOOD | 3/2-W-3/2-W-W | DO宫-RE♯清商-MI♯清角-SO♯清徵-LA♯清羽 | 0-3-5-8-10 | T0黄钟P1-T3夹钟m3-T5仲吕P4-T8夷则m6-TA无射m7 |
| SO徵FIRE | W-3/2-W-W-3/2 | DO宫-RE商-MI♯清角-SO徵-LA羽 | 0-2-5-7-9 | T0黄钟P1-T2太簇M2-T5仲吕P4-T7林钟P5-T9南吕M6 |
| LA羽WATER | 3/2-W-W-3/2-W | DO宫-RE♯清商-MI♯清角-SO徵-LA清羽 | 0-3-5-7-10 | T0黄钟P1-T3夹钟m3-T5仲吕P4-T7林钟P5-TA无射m7 |
Qi begins in the East and moves clockwise. KEYS begins in the West and moves counterclockwise. ⊖⚋YIN and ⊕⚊YANG intertwine, generating transformations. Qi begins in the East, the four seasons start with ㊍WOOD, pass to ㊋FIRE, pass to ㊏EARTH, pass to ㊎METAL, pass to ㊌WATER in sequence. KEYS begins in the West, the five notes start with ㊎METAL, pass to ㊋FIRE, pass to ㊍WOOD, pass to ㊌WATER, pass to ㊏EARTH.
| SEXAGENERY-CYCLE | FIVE-PHASES | KEYS |
|---|---|---|
| 00S0B0甲子 | ㊎METAL | RE商METAL Mode on Tonic T0黄钟P1 |
| 01S1B1乙丑 | ㊎METAL | RE商METAL Mode on Tonic T1大吕m2 |
| 02S2B2丙寅 | ㊋FIRE | SO徵FIRE Mode on Tonic T2太簇M2 |
| 03S3B3丁卯 | ㊋FIRE | SO徵FIRE Mode on Tonic T3夹钟m3 |
| 04S4B4戊辰 | ㊍WOOD | MI角WOOD Mode on Tonic T4姑洗M3 |
| 05S5B5己巳 | ㊍WOOD | MI角WOOD Mode on Tonic T5仲吕P4 |
| 06S6B6庚午 | ㊏EARTH | DO宫EARTH Mode on Tonic T6蕤宾TT |
| 07S7B7辛未 | ㊏EARTH | DO宫EARTH Mode on Tonic T7林钟P5 |
| 08S8B8壬申 | ㊎METAL | RE商METAL Mode on Tonic T8夷则m6 |
| 09S9B9癸酉 | ㊎METAL | RE商METAL Mode on Tonic T9南吕M6 |
| 10S0B10甲戌 | ㊋FIRE | SO徵FIRE Mode on Tonic TA无射m7 |
| 11S1B11乙亥 | ㊋FIRE | SO徵FIRE Mode on Tonic TB应钟M7 |
| 12S2B0丙子 | ㊌WATER | LA羽WATER Mode on Tonic T0黄钟P1 |
| 13S3B1丁丑 | ㊌WATER | LA羽WATER Mode on Tonic T1大吕m2 |
| 14S4B2戊寅 | ㊏EARTH | DO宫EARTH Mode on Tonic T2太簇M2 |
| 15S5B3己卯 | ㊏EARTH | DO宫EARTH Mode on Tonic T3夹钟m3 |
| 16S6B4庚辰 | ㊎METAL | RE商METAL Mode on Tonic T4姑洗M3 |
| 17S7B5辛巳 | ㊎METAL | RE商METAL Mode on Tonic T5仲吕P4 |
| 18S8B6壬午 | ㊍WOOD | MI角WOOD Mode on Tonic T6蕤宾TT |
| 19S9B7癸未 | ㊍WOOD | MI角WOOD Mode on Tonic T7林钟P5 |
| 20S0B8甲申 | ㊌WATER | LA羽WATER Mode on Tonic T8夷则m6 |
| 21S1B9乙酉 | ㊌WATER | LA羽WATER Mode on Tonic T9南吕M6 |
| 22S2B10丙戌 | ㊏EARTH | DO宫EARTH Mode on Tonic TA无射m7 |
| 23S3B11丁亥 | ㊏EARTH | DO宫EARTH Mode on Tonic TB应钟M7 |
| 24S4B0戊子 | ㊋FIRE | SO徵FIRE Mode on Tonic T0黄钟P1 |
| 25S5B1己丑 | ㊋FIRE | SO徵FIRE Mode on Tonic T1大吕m2 |
| 26S6B2庚寅 | ㊍WOOD | MI角WOOD Mode on Tonic T2太簇M2 |
| 27S7B3辛卯 | ㊍WOOD | MI角WOOD Mode on Tonic T3夹钟m3 |
| 28S8B4壬辰 | ㊌WATER | LA羽WATER Mode on Tonic T4姑洗M3 |
| 29S9B5癸巳 | ㊌WATER | LA羽WATER Mode on Tonic T5仲吕P4 |
| 30S0B6甲午 | ㊎METAL | RE商METAL Mode on Tonic T6蕤宾TT |
| 31S1B7乙未 | ㊎METAL | RE商METAL Mode on Tonic T7林钟P5 |
| 32S2B8丙申 | ㊋FIRE | SO徵FIRE Mode on Tonic T8夷则m6 |
| 33S3B9丁酉 | ㊋FIRE | SO徵FIRE Mode on Tonic T9南吕M6 |
| 34S4B10戊戌 | ㊍WOOD | MI角WOOD Mode on Tonic TA无射m7 |
| 35S5B11己亥 | ㊍WOOD | MI角WOOD Mode on Tonic TB应钟M7 |
| 36S6B0庚子 | ㊏EARTH | DO宫EARTH Mode on Tonic T0黄钟P1 |
| 37S7B1辛丑 | ㊏EARTH | DO宫EARTH Mode on Tonic T1大吕m2 |
| 38S8B2壬寅 | ㊎METAL | RE商METAL Mode on Tonic T2太簇M2 |
| 39S9B3癸卯 | ㊎METAL | RE商METAL Mode on Tonic T3夹钟m3 |
| 40S0B4甲辰 | ㊋FIRE | SO徵FIRE Mode on Tonic T4姑洗M3 |
| 41S1B5乙巳 | ㊋FIRE | SO徵FIRE Mode on Tonic T5仲吕P4 |
| 42S2B6丙午 | ㊌WATER | LA羽WATER Mode on Tonic T6蕤宾TT |
| 43S3B7丁未 | ㊌WATER | LA羽WATER Mode on Tonic T7林钟P5 |
| 44S4B8戊申 | ㊏EARTH | DO宫EARTH Mode on Tonic T8夷则m6 |
| 45S5B9己酉 | ㊏EARTH | DO宫EARTH Mode on Tonic T9南吕M6 |
| 46S6B10庚戌 | ㊎METAL | RE商METAL Mode on Tonic TA无射m7 |
| 47S7B11辛亥 | ㊎METAL | RE商METAL Mode on Tonic TB应钟M7 |
| 48S8B0壬子 | ㊍WOOD | MI角WOOD Mode on Tonic T0黄钟P1 |
| 49S9B1癸丑 | ㊍WOOD | MI角WOOD Mode on Tonic T1大吕m2 |
| 50S0B2甲寅 | ㊌WATER | LA羽WATER Mode on Tonic T2太簇M2 |
| 51S1B3乙卯 | ㊌WATER | LA羽WATER Mode on Tonic T3夹钟m3 |
| 52S2B4丙辰 | ㊏EARTH | DO宫EARTH Mode on Tonic T4姑洗M3 |
| 53S3B5丁巳 | ㊏EARTH | DO宫EARTH Mode on Tonic T5仲吕P4 |
| 54S4B6戊午 | ㊋FIRE | SO徵FIRE Mode on Tonic T6蕤宾TT |
| 55S5B7己未 | ㊋FIRE | SO徵FIRE Mode on Tonic T7林钟P5 |
| 56S6B8庚申 | ㊍WOOD | MI角WOOD Mode on Tonic T8夷则m6 |
| 57S7B9辛酉 | ㊍WOOD | MI角WOOD Mode on Tonic T9南吕M6 |
| 58S8B10壬戌 | ㊌WATER | LA羽WATER Mode on Tonic TA无射m7 |
| 59S9B11癸亥 | ㊌WATER | LA羽WATER Mode on Tonic TB应钟M7 |
Kaoyuan (Investigation of Origins) ctext states:
- Organized by beginning with Qi (energy) and ending with form, following the sequence of ㊌WATER, ㊋FIRE, ㊍WOOD, ㊎METAL, and ㊏EARTH as described in the Hongfan.
- Organized by their generation across the four seasons, they follow the sequence of ㊍WOOD, ㊋FIRE, ㊏EARTH, ㊎METAL, and ㊌WATER as found in the Yueling.
- Arranged based on the control and balance of materials, the sequence is ㊌WATER, ㊋FIRE, ㊎METAL, ㊍WOOD, and ㊏EARTH as seen in Yu’s Plan.
However, KEYS Five PHASES begin with ㊎METAL, followed by ㊋FIRE, then ㊍WOOD, ㊌WATER, and ㊏EARTH. This sequence neither adheres to the order of beginning and ending, nor does it derive from the principles of generation or control. Thus, commentators have been perplexed about its origin. Upon detailed examination, its meaning seems to trace back to the symbolic ideas of the Yi (Book of Changes), specifically aligning with the principles of the PRENATAL and POSTNATAL EIGHT-TRIGRAMES. To clarify this, separate diagrams can be made to illustrate these relationships.
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KEYS FIVE-PHASES correspondence with PRENATAL EIGHT-TRIGRAM DIAGRAM
In the PRENATAL EIGHT-TRIGRAM DIAGRAM, ☰HEAVEN and ☱LAKE take the lead, belonging to ㊎METAL. Next comes ☲FIRE, belonging to ㊋FIRE, followed by ☳THUNDER and ☴WIND, belonging to ㊍WOOD. Then comes ☵WATER, belonging to ㊌WATER, and finally ☶MOUNTAIN and ☷EARTH, belonging to ㊏EARTH. This sequence begins with ㊎METAL and ends with ㊏EARTH, embodying the principle of “☰HEAVEN initiates, ☷EARTH completes.” ㊎METAL represents the firmness of Heaven, ㊏EARTH embodies the softness of the Earth, ㊋FIRE aligns with Heaven, ㊌WATER aligns with Earth, and ㊍WOOD, as the essence of life, occupies the central position. This sequence of KEYS is rooted in the order of the PRENATAL EIGHT-TRIGRAM DIRECTION.
KEYS FIVE-PHASES correspondence with POSTNATAL EIGHT-TRIGRAM DIAGRAM
In the POSTNATAL EIGHT-TRIGRAM DIAGRAM, ☰HEAVEN also takes the lead, but the sequence is reversed. Starting from ☰HEAVEN and ☱LAKE, ㊎METAL prospers in the West. It then transitions to ☲FIRE, where ㊋FIRE prospers in the South. Next, it moves to ☳THUNDER and ☴WIND, where ㊍WOOD prospers in the East, followed by ☵WATER, where ㊌WATER prospers in the North. ㊏EARTH prospers during the four seasons, and thus ☶MOUNTAIN and ☷EARTH are placed at the end. This arrangement of KEYS is rooted in the order of the POSTNATAL EIGHT-TRIGRAM DIRECTION.
The Na Yin Five Elements Divided into Three Cycles Corresponding to Musical Notes and Generating Each Other Across Eight Intervals
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Starting with 00S0B0甲子 and 01S1B1乙丑 as the 3C-0上元UPPER-CYCLE of ㊎METAL, followed by 08S8B8壬申 and 09S9B9癸酉 as the 3C-1中元MIDDLE-CYCLE of ㊎METAL, and then 16S6B4庚辰 and 17S7B5辛巳 as the 3C-2下元LOWER-CYCLE of ㊎METAL, the THREE-CYCLES are completed. The sequence then transitions to the ㊋FIRE, beginning with 24S4B0戊子 and 25S5B1己丑 as the 3C-0上元UPPER-CYCLE of ㊋FIRE, Bingshen (丙申) and Dingyou (丁酉) as the 3C-1中元MIDDLE-CYCLE of ㊋FIRE, and Jiachen (甲辰) and Yisi (乙巳) as the 3C-2下元LOWER-CYCLE of ㊋FIRE. From this point onward, the sequence follows the progression of ㊎METAL, ㊋FIRE, ㊍WOOD, ㊌WATER, ㊏EARTH, as shown in the previous diagram. It adopts the principle of aligning with musical tones and uses the method of “same position marriage, generating across eight intervals” to complete the SMALL-CYCLE of MUSCIAL-KEYS, ending at 53S3B5丁巳. Subsequently, starting with 30S0B6甲午 and 31S1B7乙未 as the 3C-0上元UPPER-CYCLE of ㊎METAL, and following the same method, the sequence concludes at 23S3B11丁亥, completing the LARGE CYCLE of MUSICAL-KEYS.