納音 Na-Yin

沈括曰六十甲子有納音鮮原其意蓋六十律旋相為宫法也一律含五音十二律納六十音也凡氣始於東方而右行音起於西方而左行隂陽相錯而生變化所謂氣始於東方者四時始於木右行傳於火火傳於土土傳於金金傳於水所謂音始於西方者五音始於金左旋傳于火火傳于木木傳于水水傳於土_{納音與易納甲同法乾納甲而坤納癸始于乾而終于坤納音始于金金乾也終于土土坤也}

納音之法同類娶妻隔八生子此律呂相生之法也五行先仲而後孟孟而後季此遁甲三元之紀也甲子金之仲_黄鐘之商同位娶乙丑_{大呂之商同位謂甲與乙丙與丁之類下皆倣此}隔八下生壬申金之孟_{夷則之商隔八謂大呂下生夷則也下皆倣此}壬申同位娶癸酉_南呂之商隔八上生庚辰金之季_{姑洗之商此金三元終若只以陽辰言之則依遁甲順傳仲孟季若兼妻言之則逆傳孟仲季也}庚辰同位娶辛巳_仲呂之商隔八下生戊子火之仲_{黄鐘之徵金三元終則左行傳南方火也}戊子娶己丑_大呂之徵生丙申火之孟_夷則之徵丙申娶丁酉_南呂之徵生甲辰火之季_姑洗之徵甲辰娶乙巳_仲呂之徵生壬子木之仲_{黄鐘之角火三元終則左行傳于東方木}如是左行至於丁巳仲呂之宫五音一終復自甲午金之仲娶乙未隔八生壬寅一如甲子之法終於癸亥_{謂蕤賓娶林鐘上生太簇之類}子至於巳為陽故自黄鐘至於仲呂皆下生自午至於亥為隂故自林鐘至於應鐘皆上生

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.

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.

干支 _Sexagenery	五行 _NA-YIN	孟仲季 _Place	兩儀 _{Elementary Forms}	律 _Tone	音 _Mode
^00H0E0甲子	^X3金</sub>	^1ST孟	陽⚊_{0 YANG}	^T0黄鐘	^RE商
^01H1E1乙丑	^X3金</sub>	^1ST孟	陽⚊_{0 YANG}	^T1大呂	^RE商
^02H2E2丙寅	^X1火</sub>	^2ND仲	隂⚋_{1 YIN}	^T2泰簇	^SO徵
^03H3E3丁卯	^X1火</sub>	^2ND仲	隂⚋_{1 YIN}	^T3夾鐘	^SO徵
^04H4E4戊辰	^X0木</sub>	^3RD季	陽⚊_{0 YANG}	^T4姑洗	^MI角
^05H5E5己巳	^X0木</sub>	^3RD季	陽⚊_{0 YANG}	^T5仲呂	^MI角
^06H6E6庚午	^X2土</sub>	^1ST孟	隂⚋_{1 YIN}	^T6蕤賓	^DO宫
^07H7E7辛未	^X2土</sub>	^1ST孟	隂⚋_{1 YIN}	^T7林鐘	^DO宫
^08H8E8壬申	^X3金</sub>	^2ND仲	陽⚊_{0 YANG}	^T8夷則	^RE商
^09H9E9癸酉	^X3金</sub>	^2ND仲	陽⚊_{0 YANG}	^T9南呂	^RE商
^10H0E↊甲戌	^X1火</sub>	^3RD季	隂⚋_{1 YIN}	^T↊無射	^SO徵
^11H1E↋乙亥	^X1火</sub>	^3RD季	隂⚋_{1 YIN}	^T↋應鐘	^SO徵
^12H2E0丙子	^X4水</sub>	^1ST孟	陽⚊_{0 YANG}	^T0黄鐘	^LA羽
^13H3E1丁丑	^X4水</sub>	^1ST孟	陽⚊_{0 YANG}	^T1大呂	^LA羽
^14H4E2戊寅	^X2土</sub>	^2ND仲	隂⚋_{1 YIN}	^T2泰簇	^DO宫
^15H5E3己卯	^X2土</sub>	^2ND仲	隂⚋_{1 YIN}	^T3夾鐘	^DO宫
^16H6E4庚辰	^X3金</sub>	^3RD季	陽⚊_{0 YANG}	^T4姑洗	^RE商
^17H7E5辛巳	^X3金</sub>	^3RD季	陽⚊_{0 YANG}	^T5仲呂	^RE商
^18H8E6壬午	^X0木</sub>	^1ST孟	隂⚋_{1 YIN}	^T6蕤賓	^MI角
^19H9E7癸未	^X0木</sub>	^1ST孟	隂⚋_{1 YIN}	^T7林鐘	^MI角
^20H0E8甲申	^X4水</sub>	^2ND仲	陽⚊_{0 YANG}	^T8夷則	^LA羽
^21H1E9乙酉	^X4水</sub>	^2ND仲	陽⚊_{0 YANG}	^T9南呂	^LA羽
^22H2E↊丙戌	^X2土</sub>	^3RD季	隂⚋_{1 YIN}	^T↊無射	^DO宫
^23H3E↋丁亥	^X2土</sub>	^3RD季	隂⚋_{1 YIN}	^T↋應鐘	^DO宫
^24H4E0戊子	^X1火</sub>	^1ST孟	陽⚊_{0 YANG}	^T0黄鐘	^SO徵
^25H5E1己丑	^X1火</sub>	^1ST孟	陽⚊_{0 YANG}	^T1大呂	^SO徵
^26H6E2庚寅	^X0木</sub>	^2ND仲	隂⚋_{1 YIN}	^T2泰簇	^MI角
^27H7E3辛卯	^X0木</sub>	^2ND仲	隂⚋_{1 YIN}	^T3夾鐘	^MI角
^28H8E4壬辰	^X4水</sub>	^3RD季	陽⚊_{0 YANG}	^T4姑洗	^LA羽
^29H9E5癸巳	^X4水</sub>	^3RD季	陽⚊_{0 YANG}	^T5仲呂	^LA羽
^30H0E6甲午	^X3金</sub>	^1ST孟	隂⚋_{1 YIN}	^T6蕤賓	^RE商
^31H1E7乙未	^X3金</sub>	^1ST孟	隂⚋_{1 YIN}	^T7林鐘	^RE商
^32H2E8丙申	^X1火</sub>	^2ND仲	陽⚊_{0 YANG}	^T8夷則	^SO徵
^33H3E9丁酉	^X1火</sub>	^2ND仲	陽⚊_{0 YANG}	^T9南呂	^SO徵
^34H4E↊戊戌	^X0木</sub>	^3RD季	隂⚋_{1 YIN}	^T↊無射	^MI角
^35H5E↋己亥	^X0木</sub>	^3RD季	隂⚋_{1 YIN}	^T↋應鐘	^MI角
^36H6E0庚子	^X2土</sub>	^1ST孟	陽⚊_{0 YANG}	^T0黄鐘	^DO宫
^37H7E1辛丑	^X2土</sub>	^1ST孟	陽⚊_{0 YANG}	^T1大呂	^DO宫
^38H8E2壬寅	^X3金</sub>	^2ND仲	隂⚋_{1 YIN}	^T2泰簇	^RE商
^39H9E3癸卯	^X3金</sub>	^2ND仲	隂⚋_{1 YIN}	^T3夾鐘	^RE商
^40H0E4甲辰	^X1火</sub>	^3RD季	陽⚊_{0 YANG}	^T4姑洗	^SO徵
^41H1E5乙巳	^X1火</sub>	^3RD季	陽⚊_{0 YANG}	^T5仲呂	^SO徵
^42H2E6丙午	^X4水</sub>	^1ST孟	隂⚋_{1 YIN}	^T6蕤賓	^LA羽
^43H3E7丁未	^X4水</sub>	^1ST孟	隂⚋_{1 YIN}	^T7林鐘	^LA羽
^44H4E8戊申	^X2土</sub>	^2ND仲	陽⚊_{0 YANG}	^T8夷則	^DO宫
^45H5E9己酉	^X2土</sub>	^2ND仲	陽⚊_{0 YANG}	^T9南呂	^DO宫
^46H6E↊庚戌	^X3金</sub>	^3RD季	隂⚋_{1 YIN}	^T↊無射	^RE商
^47H7E↋辛亥	^X3金</sub>	^3RD季	隂⚋_{1 YIN}	^T↋應鐘	^RE商
^48H8E0壬子	^X0木</sub>	^1ST孟	陽⚊_{0 YANG}	^T0黄鐘	^MI角
^49H9E1癸丑	^X0木</sub>	^1ST孟	陽⚊_{0 YANG}	^T1大呂	^MI角
^50H0E2甲寅	^X4水</sub>	^2ND仲	隂⚋_{1 YIN}	^T2泰簇	^LA羽
^51H1E3乙卯	^X4水</sub>	^2ND仲	隂⚋_{1 YIN}	^T3夾鐘	^LA羽
^52H2E4丙辰	^X2土</sub>	^3RD季	陽⚊_{0 YANG}	^T4姑洗	^DO宫
^53H3E5丁巳	^X2土</sub>	^3RD季	陽⚊_{0 YANG}	^T5仲呂	^DO宫
^54H4E6戊午	^X1火</sub>	^1ST孟	隂⚋_{1 YIN}	^T6蕤賓	^SO徵
^55H5E7己未	^X1火</sub>	^1ST孟	隂⚋_{1 YIN}	^T7林鐘	^SO徵
^56H6E8庚申	^X0木</sub>	^2ND仲	陽⚊_{0 YANG}	^T8夷則	^MI角
^57H7E9辛酉	^X0木</sub>	^2ND仲	陽⚊_{0 YANG}	^T9南呂	^MI角
^58H8E↊壬戌	^X4水</sub>	^3RD季	隂⚋_{1 YIN}	^T↊無射	^LA羽
^59H9E↋癸亥	^X4水</sub>	^3RD季	隂⚋_{1 YIN}	^T↋應鐘	^LA羽

律呂 _Tone	_{1/3 Loss and Gain}	12 TET	Just intonation _wiki	Pythagorean tuning _wiki
^T0黄钟_B♯	C</sub>	1/1	2^(0/12)	⁠1/1⁠	1/1
^T1大吕_C♯	D♭</sub>	(3/2)^4 * (3/4)^3	2^(1/12)	⁠16/15⁠	(2/3)^5 * 2^3
^T2太簇_D	3/2 * 3/4	2^(2/12)	⁠9/8⁠	(3/2)^2 * 1/2
^T3夹钟_D♯	E♭</sub>	(3/2)^5 * (3/4)^4	2^(3/12)	⁠6/5⁠	(2/3)^3 * 2^2
^T4姑洗_E	F♭</sub>	(3/2)^2 * (3/4)^2	2^(4/12)	⁠5/4	(3/2)^4 * (1/2)^2
^T5仲吕_E♯	F</sub>	(3/2)^6 * (3/4)^5	2^(5/12)	⁠4/3	2/3 * 2
^T6蕤宾_F♯	G♭</sub>	(3/2)^3 * (3/4)^3	2^(6/12)	⁠64/45	(2/3)^6 * 2^4 and (3/2)^6 * (1/2)^3
^T7林钟_G	3/2	2^(7/12)	⁠3/2	3/2
^T8夷则_G♯	A♭</sub>	(3/2)^4 * (3/4)^4	2^(8/12)	⁠8/5	(2/3)^4 * 2^3
^T9南吕_A	(3/2)^2 * 3/4	2^(9/12)	⁠5/3⁠	(3/2)^3 * 1/2
^T↊无射_A♯	B♭</sub>	(3/2)^5 * (3/4)^5	2^(10/12)	⁠16/9⁠	(2/3)^2 * 2^2
^T↋应钟_B	C♭</sub>	(3/2)^3 * (3/4)^2	2^(11/12)	⁠15/8	(3/2)^5 * (1/2)^2
^T0黄钟_B♯	C</sub>	(3/2)^6 * (3/4)^6	2^(12/12)	⁠2/1	2/1

Mode	1st note	2nd note	3rd note	4th note	5th note
^X2宫_{EARTH Major}	^DO宫	^RE商	^MI角	^SO徵	^LA羽
	^I0純一度_P1	^I2大二度_M2	^I4大三度_M3	^I7純五度_P5	^T9大六度_M6
^X3商_{METAL Suspended}	^RE商	^MI角	^SO徵	^LA羽	^DO宫
	^I0純一度_P1	^I2大二度_M2	^I5純四度_P4	^I7純五度_P5	^I↊小七度_m7
^X0角_{WOOD Blues Minor}	^MI角	^SO徵	^LA羽	^DO宫	^RE商
	^I0純一度_P1	^I3小三度_m3	^I5純四度_P4	^I8小六度_m6	^I↊小七度_m7
^X1徵_{FIRE Blues Major}	^SO徵	^LA羽	^DO宫	^RE商	^MI角
	^I0純一度_P1	^I2大二度_M2	^I5純四度_P4	^I7純五度_P5	^I9大六度_M6
^X4羽_{WATER Minor}	^LA羽	^DO宫	^RE商	^MI角	^SO徵
	^I0純一度_P1	^I3小三度_m3	^I5純四度_P4	^I7純五度_P5	^I↊小七度_m7

蠡海集曰萬物之所為以生者必由氣氣者何金也金受氣順行則為五行之體逆行則為五行之用順行為五行之體者金生水水生木木生火火生土冬至起歷之元自冬而春春而夏夏而長夏長夏而歸於秋返本歸原而收斂也逆行為五行之用者金出鑛而從革於火以成材成材則為有生之用然火非木不生必循木以繼之木必依水以滋榮水必托土以止畜故木而水水而土是則四行之類土以定位故大撓作甲子分配五行為納音蓋金能受聲而宣氣故也法曰甲娶乙妻隔八生子子生孫而後行繼代其位初一曰金金為氣居先甲子為受氣之始甲娶乙妻隔八壬申是為子矣壬娶癸妻隔八庚辰是為孫矣庚娶辛妻隔八戊子火代其位次二曰火戊繼其後戊娶己妻隔八丙申是為子矣丙娶丁妻隔八甲辰是為孫矣甲娶乙妻隔八壬子木代其位次三曰木壬繼其後壬娶癸妻隔八庚申是為子矣庚娶辛妻隔八戊辰是為孫矣戊娶己妻隔八丙子水代其位次四曰水丙繼其後丙娶丁妻隔八甲申是為子矣甲娶乙妻隔八壬辰是為孫矣壬娶癸妻隔八庚子土代其位次五曰土庚娶辛妻隔八戊申是為子矣戊娶己妻隔八丙辰是為孫矣丙娶丁妻隔八甲子金復代其位甲午乙未起如前法是故有五子歸庚之說道家者流取其義用配五方之位自子干頭數至庚字則為其數甲子金自甲數至七逢庚則西方金得七氣戊子火自戊數至三逢庚則南方火得三氣壬子木自壬數至九逢庚則東方木得九氣丙子水自丙數至五逢庚則北方水得五氣庚子土則自得一為中方一氣是為五子歸庚也乃知金者受氣之先順行則為五行之體逆行則為五行之用故六十甲子納音者以充萬物之用

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.

考原曰五行以氣始形終為次則洪範之水火木金土是也以播於四時相生為次則月令之木火土金水是也以飭庀五材相尅為次則禹謨之水火金木土是也納音五行始金次火次木次水次土既非本其始終又無取於生尅故說者莫知其所自來詳考其義蓋亦祖述易象之意即先後天卦之理也各為圖以明之

納音五行應先天圖 NA-Yin x Pre-Trigrams

先天之圖乾兌居首屬金次以離屬火又次震巽屬木又次以坎屬水終於艮坤屬土故始於金終於土者乾始坤成之義也金取於天之剛土取於地之柔火附於天水附於地而木以生氣居中此納音所本於先天之序也

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.

納音五行應後天圖 NA-Yin x Post-Trigrams

後天之圖亦以乾居首而逆轉自乾兌之金旺於西方次轉而為離火旺於南方次又轉而為震巽之木旺於東方次又轉而為坎水旺於北方而土旺於四季故退艮坤以居終焉此納音所本於後天之序也

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.

納音五行分三元應樂律隔八相生圖 The Na Yin Five Elements Divided into Three Cycles Corresponding to Musical Notes and Generating Each Other Across Eight Intervals

右圖以甲子乙丑為金上元壬申癸酉為金中元庚辰辛巳為金下元三元俱周則傳於戊子己丑為火上元丙申丁酉為火中元甲辰乙巳為火下元自此以後皆依前圖金火木水土之次而用樂律同位娶妻隔八生子之法以終於丁巳而納音小成矣又自甲午乙未為金上元起如前法以終於丁亥而納音大成矣

按十干十二支相錯為六十五音十二律相乘亦為六十甲子金而乙丑亦為金者同位娶妻也乙丑金而壬申又為金者隔八生子也一行各三元而後傳於次行猶春有孟仲季三月而後傳於夏也自甲子至丁巳而五行之三元一周猶易之三畫為小成也自甲午至丁亥而五行之三元又一周猶易之六畫為大成也其立法皆與律呂相應

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.

納音干支起數合五行

甲己子午九乙庚丑未八丙辛寅申七丁壬卯酉六戊癸辰戌五巳亥屬四數

蠡海集云或問曰先天之數何緣而起余答曰數極於九自九逆退取之故甲己子午九乙庚丑未八丙辛寅申七丁壬卯酉六戊癸辰戌五天干已盡而地支獨遺巳亥是以巳亥得四終焉况夫亥為天門巳為地戶純陽之位為開闔之樞所以關鍵五行也

瑞桂堂暇録曰六十甲子之納音以金木水火土之音而明之也一六為水二七為火三八為木四九為金五十為土然五行之中惟金木有自然之音水火土必相假而後成音蓋水假土火假水土假火故金音四九木音三八水音五十火音一六土音二七此不易之論也何以言之甲己子午九也乙庚丑未八也丙辛寅申七也丁壬卯酉六也戊癸辰戌五也巳亥四也甲子乙丑其數三十有四四者金之音也故曰金戊辰己巳其數二十有三三者木之音也故曰木庚午辛未其數三十有二二者火也土以火為音故曰土甲申乙酉其數三十十者土也水以土為音故曰水戊子己丑其數三十有一一者水也火以水為音故曰火凡六十甲子莫不皆然此納音之所由起也

考原曰此揚子雲太玄論聲律所紀數也凡兩干兩支之合其餘數得四九者為金得一六者為火得三八者為木得五十者為水得二七者為土如甲子皆九得數十八乙丑皆八得數十六合之三十有四故為金壬六申七得數十三癸五酉六得數十一合之二十有四故亦為金也其餘按數推之莫不皆然但所配一六二七等數與河圖之數不同今按大衍之數五十其用四十有九以兩干兩支之合數於四十九内減之餘數滿十去之餘一六為水二七為火三八為木四九為金五十為土各取所生之五行以為納音如是則與河圖相同又揲蓍之法用餘策以定奇偶此用餘數以定五行其理正相合也如甲九子九乙八丑八其合數三十四於四十九内減之餘十五十不用餘五屬土土生金故曰金丙寅丁卯共合數二十六於四十九内減之餘二十三十不用餘三屬木木生火故曰火戊辰己巳共合數二十三於四十九内減之餘二十六十不用餘六屬水水生木故曰木庚午辛未共合數三十二於四十九内減之餘十七十不用餘七屬火火生土故曰土餘倣此按揚雄太玄經曰子午之數九丑未八寅申七卯酉六辰戌五己亥四故律四十二呂三十六并律呂之數或還或否凡七十有八黄鐘之數立焉其以為度也皆生黄鐘又曰甲己之數九乙庚八丙辛七丁壬六戊癸五聲生於日律生於辰聲以情質律以和聲聲律相協而八音生歷代以來宗之謂之先天之數顧其甲己子午之何以九乙庚丑未之何以八則罕有確論焉今按子午者乾震之所納也丑未者坤巽之所納也寅申者坎所納也卯酉者離所納也辰戌者艮所納也巳亥者兌所納也陽數極於九隂數極於八故乾坤得之震巽長而統於父母其餘以次而降兩大六子男女長少之序秩然不紊實非人之能強為也若夫十日之序則又各隨化氣壽夭之數而亦無一毫造作於其間甲己土也土終古不毁即析為微塵蕩為鄰虚而其質固在也為最壽故數九其次則金雖火鑠之亦有質灰氣散之時而堅固為萬物王也乙庚金也故次甲己也又次則水日炙風銷而火煎烹之亦有乾盡之時而無自然銷滅之期雖其堅固不若金而其柔弱轉能久壽而物莫若也丙辛水也故次乙庚也又次則木一歲之中榮落有定期也丁壬木也故次丙辛也又次則火一晝夜間顯晦有定期也戊癸火也故次丁壬也且甲己土生乙庚金乙庚金生丙辛水丙辛水生丁壬木丁壬木生戊癸火層累而下之又自然而然之數也然則無十無一二三何也曰數終於九十即一也若夫一二三乃天地人之大數不得偏寄於一日一辰之間者也且言九八七六五四則一二三在其中也故黄鐘八十一十二辰止得七十八而揚子曰黄鐘之數立焉蓋已虚函三數而成八十一也

五行五音

宫 _屬土生金 _{甲子乙丑　壬申癸酉　庚辰辛巳　甲午乙未　壬寅癸卯　庚戌辛亥}

商 _屬金生水 _{丙子丁丑　甲申乙酉　壬辰癸巳　丙午丁未　甲寅乙卯　壬戌癸亥}

角 _屬木生火 _{戊子己丑　丙申丁酉　甲辰乙巳　戊午己未　丙寅丁卯　甲戌乙亥}

徵 _屬火生土 _{庚子辛丑　戊申己酉　丙辰丁巳　庚午辛未　戊寅己卯　丙戌丁亥}

羽 _屬水生木 _{壬子癸丑　庚申辛酉　戊辰己巳　壬午癸未　庚寅辛卯　戊戌己亥}

朱子曰樂聲是土金木火水洪範是水火木金土蓋納音者以干支分配於五音而本音所生之五行即為其干支所納之音也初一宫商角徵羽納甲丙戊庚壬係以五子而隨以五丑宫得甲子商得丙子角得戊子徵得庚子羽得壬子宫為土土生金故甲子乙丑納音金商為金金生水故丙子丁丑納音水角為木木生火故戊子己丑納音火徵為火火生土故庚子辛丑納音土羽為水水生木故壬子癸丑納音木次二商角徵羽宫納甲丙戊庚壬係以五寅而隨以五卯商金得甲寅乙卯納音水角木得丙寅丁卯納音火徵火得戊寅己卯納音土羽水得庚寅辛卯納音木宫土得壬寅癸卯納音金次三角徵羽宫商納甲丙戊庚壬係以五辰而隨以五巳角木得甲辰乙巳納音火徵火得丙辰丁巳納音土羽水得戊辰己巳納音木宫土得庚辰辛巳納音金商金得壬辰癸巳納音水以上六甲得其半納音小成次四復以宫商角徵羽納甲丙戊庚壬係以五午而隨以五未宫土得甲午乙未納音金商金得丙午丁未納音水角木得戊午己未納音火徵火得庚午辛未納音土羽水得壬午癸未納音木次五復以商角徵羽宫納甲丙戊庚壬係以五申而隨以五酉商金得甲申乙酉納音水角木得丙申丁酉納音火徵火得戊申己酉納音土羽水得庚申辛酉納音木宫土得壬申癸酉納音金次六復以角徵羽宫商納甲丙戊庚壬係以五戌而隨以五亥角木得甲戌乙亥納音火徵火得丙戌丁亥納音土羽水得戊戌己亥納音木宫土得庚戌辛亥納音金商金得壬戌癸亥納音水於是六甲全而納音大成矣陽生於子自甲子以至癸巳隂生於午自甲午以至癸亥故三十而復從宫起宫君商臣角民皆人道也故皆可以為首徵事羽物皆人所用也故不可以為首是以三甲終而復始於宫干為天支為地音為人三才之五行備矣

陶宗儀曰

甲子乙丑海中金者子屬水又為湖又為水旺之地兼金死於子墓於丑水旺而金死墓故曰海中金也

丙寅丁卯鑪中火者寅為三陽卯為四陽火既得地又得寅卯之木以生之此時天地開鑪萬物始生故曰鑪中火也

戊辰己巳大林木者辰為原野已為六陽木至六陽則枝榮葉茂以茂盛之木而在原野之間故曰大林木也

庚午辛未路傍土者未中之木而生午位之旺火火旺則土焦未能育物猶路傍土若也故曰路傍土也

壬申癸酉劍鋒金者申酉金之正位兼臨官申帝旺酉金既生旺則成剛矣剛則無踰於劍鋒故曰劍鋒金也

甲戌乙亥山頭火者戌亥為天門火照天門其光至高故曰山頭火也

丙子丁丑澗下水者水旺於子衰於丑旺而反衰則不能為江河故曰澗下水也

戊寅己卯城頭土者天干戊巳屬土寅為艮山土積而為山故曰城頭土也

庚辰辛巳白鑞金者金養於辰生於巳形質初成未能堅利故曰白鑞金也

壬午癸未楊柳木者木死於午墓於未木既死墓雖得天干壬癸之水以生之終是柔弱故曰楊柳木也

甲申乙酉井泉水者金臨官申帝旺酉金既生旺則水由以生然方生之際力量未洪故曰井泉水也

丙戌丁亥屋上土者丙丁屬火戌亥為天門火既炎上則土非在下而生故曰屋上土也

戊子己丑霹靂火者丑屬土子屬水水居正位而納音乃火水中之火非神龍則無故曰霹靂火也

庚寅辛卯松栢木者木臨官寅帝旺卯木既生旺則非柔弱之比故曰松栢木也

壬辰癸巳長流水者辰為水庫巳為金長生之地金生則水性已存以庫水而逢生金則泉源終不竭故曰長流水也

甲午乙未砂石金者午為火旺之地火旺則金敗未為火衰之地火衰則金冠帶敗而方冠帶未能盛滿故曰砂石金也

丙申丁酉山下火者申為地戶酉為日入之門日至此時而藏光故曰山下火也

戊戌己亥平地木者戌為原野亥為木生之地夫木生於原野則非一根一株之比故曰平地木也

庚子辛丑壁上土者丑雖土家正位而子則水旺之地土見水多則為泥也故曰壁上土也

壬寅癸卯金箔金者寅卯為木旺之地木旺則金羸又金絶於寅胎於卯金既無力故曰金箔金也

甲辰乙巳覆燈火者辰為食時已為禺中日之將中豔陽之勢光於天下故曰覆燈火也

丙午丁未天河水者丙丁屬火午為火旺之地而納音乃水水自火出非銀漢不能有也故曰天河水也

戊申己酉大驛土者申為坤坤為地酉為兌兌為澤戊巳之土加於坤澤之上非其他浮薄之土也故曰大驛土也

庚戌辛亥釵釧金者金至戌而衰至亥而病金既衰病則誠柔矣故曰釵釧金也

壬子癸丑桑柘木者子屬水丑屬金水方生木金則伐之猶桑柘木也

甲寅乙卯大溪水者寅為東北維卯為正東水流正東則其性順而川澗池沼俱合而歸故曰大溪水也

丙辰丁巳沙中土者土庫辰絶已而天干丙丁之火至辰冠帶已臨官土既庫絶旺火復與生之故曰沙中土也

戊午己未天上火者午為火旺之地未中之木又復生之火性炎上又逢生地故曰天上火也

庚申辛酉石榴木者申為七月酉為八月此時木則絶矣惟石榴之木反結實故曰石榴木也

壬戌癸亥大海水者水冠帶戌臨官亥水臨官冠帶則力厚矣兼亥為江非他水之比故曰大海水也

宫	_屬土生金	_{甲子乙丑　壬申癸酉　庚辰辛巳　甲午乙未　壬寅癸卯　庚戌辛亥}
商	_屬金生水	_{丙子丁丑　甲申乙酉　壬辰癸巳　丙午丁未　甲寅乙卯　壬戌癸亥}
角	_屬木生火	_{戊子己丑　丙申丁酉　甲辰乙巳　戊午己未　丙寅丁卯　甲戌乙亥}
徵	_屬火生土	_{庚子辛丑　戊申己酉　丙辰丁巳　庚午辛未　戊寅己卯　丙戌丁亥}
羽	_屬水生木	_{壬子癸丑　庚申辛酉　戊辰己巳　壬午癸未　庚寅辛卯　戊戌己亥}