s the loer urns on Her God imothy C. akach d donload $1.0, solo a caella rinted $.00 imothy C. akach s the loer urns on Her God or a caella choir, sora solo
ext: ena, stigme, hex, ena, ok zehyron, treis, treis, ennea, ok ok heta, tettara, ennea, ok ennea, tettara, ok tettara, ok dyo, zehyron, tettara, ente, ok hex, ok treis, tettara, treis, hex, ente, hex, treis, ok ena, ena, heta, heta, dyo, zehyron, treis, zehyron, ennea, ena, heta, ennea, ok zehyron, ente, (quintet) heta, hex, dyo, ok hex, dyo, ena, treis, ente, tettara, (tutti) tettara, ok hex, dyo, dyo, heta, zehyron, ente, dyo, hex, zehyron, tettara, hex, dyo, ok ena, (ok ennea, zehyron, dyo, tettara, tettara, ennea, heta,) decimal equivalent o hi (φ) Quidam osuit um ar ciculorum in quodam lo, qui erat dique ariete circumdat ut sciret, quot ex eo aria germinarentur in u an. ibonacci (Leonardo o isa) sg in Greek certain erson laced one air o rabbits in a certain lace that as on all sides surroded by a all, so that he might learn, ho many airs ould be roduced rom it in one year. trans. nne Groton Notes: s the loer urns on Her God translates to related mathematical concets into music the golden ratio and the ibonacci sequence. he golden ratio (hi) is a recise ratio that curs hen a line segment (+) is divided into to smaller segments, and the ratios o the larger segment () to the smaller () and the hole + segment (+) to the larger () are equal. he brilliant art is that the golden ratio curs naturally in things like roses, inecones, and other lants. It is also believed to be one o the most aesthetically leasing roortions and is sought ater and desired in art, architecture, and in this and e other cases, music. In my research, I came across a book called he Golden Ratio by Mario Livio. In one o the chaters he shos the resence o the golden ratio in the sacial distribution o leaves on lants and in the sirals od in the head o a sloer. he chater s title is s the loer urns on Her God, a line rom a homas Moore oem. he ibonacci sequence as discoverd by Leonardo o isa (ibonacci) in the early 1th century in his book Liber baci. He osed a question using the reroduction rate o rabbits as his examle, and discovered a sequence o numbers here, starting ith 1, one adds the current number to the revious number to get the next number. o 1+0=1, 1+1=, +1=, +=5, and so on. he sequence looks like this: 1, 1,,, 5, 8, 1, 1,, 55, 89, 1... Dividing a number in the ibonacci sequence by its redecessor gives us a close aroximation to hi. s you erorm this ction higher and higher in the sequence, the anser is alternately higher and loer than hi; aroaching it, but never reaching it. I assigned each number in the ibonacci sequence (u to ) to a chord based o o its corresonding scale degree. he 8th scale degree returns to tonic, so 1=i, =II, =iii, 5=v, 8=i, 1=vi, 1=vii, and =vi. hese chords ormed the rogression o the iece; starting ith one chord in the irst hrase, and then adding an additional chord o the sequence to it in each successive hrase: i, iii, iiiiii, iiiiiiiiiii, iiiiiiiviiiiiii, etc. s the iece began to take orm, I took liberties in the major or mir tonality o each chord, decidedly crossing the line rom science into art. Having made this decision, I still needed a text. art o the intrigue behind hi is that the decimal aroximation goes on orever ithout reeating, so the choir sings this number in Greek (usage o hi can be traced back to Euclid and ythagorus in ancient Greece) to 7 decimal laces (the irst ena and stigme (1.) don t cot). y the end, the rhythmic alto edal oint has extended that to 8 decmial laces. I also anted to include ibonacci s original question about rabbits, so I gave that text to the sora solo. It is the original Latin text rom his book, Liber baci. hi (decimal aroximation) 1.180988798988058858117700917 98057815870508189097... ibonacci sequence 1, 1,,, 5, 8, 1, 1,, 55, 89, 1,, 77, 10, 987... ecial thanks to thank Mario Livio, nne Groton and Marquis erry or heling me research this iece.
Dedicated to Chris akach, my irst and avorite math teacher s the loer urns on Her God or a caella div. choir lto er Leonardo o isa (ibonacci) h = 5 œ œ œ œ œ œ œ œ œ ctum, ze hy rum, vem, œ. œ œ œ or erusal uroses only. Do t use, coy, or distribute. ze hy rum,. œ œ œ œ œ ze hy rum, œ œ œ œ. c tum, œ œ œ œ œ imothy C. akach œ œ œ œ œ œ œ. se tem, quat tu vem, vem, quat tu quattu to du o 9 vem, se tem, quat tu vem, œ œ œ œ œ or erusal uroses only. Do t use, coy, or distribute. œ œ œ œ se tem, quat tu œ œ œ ze hy rum, quat tu quin que, quat tu 007 ll Rights Reserved. or more irmation and to order scores lease visit imohycakach.com
1 s the loer urns on Her God / imothy C. akach vem, b vem, œ œ œ œ œ œ quin que, tres se tem, se tem, du o, œ œ œ œ œ œ or erusal uroses only. Do t use, coy, or distribute. vem, vem, œ œ œ œ du o, ze hy œ. œ œ 1 œ œ œ. quat tu quat tu to du o œ œ b quat tu œ. œ œ œ rum, ze hy rum, vem, se tem, vem, œ œ quat tu œ œ œ œ œ œ quat tu quat tu to du o b or erusal uroses only. Do t use, coy, or distribute. n œ. to du o œ. œ.
19 ze hy rum, quat tu quin que, ze hy rum, œ œ ze hy rum, quin que, se tem, du o, ze hy rum, quat tu quin que, s the loer urns on Her God / imothy C. akach œ œ œ œ quat tu œ œ œ œ œ œ or erusal uroses only. Do t use, coy, or distribute. quat tu quin que, b quin que, œ.. œ œ œ. n dim. quat tu quin que,. œ œ œ œ œ œ œ œ du o quinque,quat tu quat tu. quin que,. œ œ quat tu œ œ quat tu œ œ œ œ œ. quin que, or erusal uroses only. Do t use, coy, or distribute. œ. tres n dim. π tres n dim. tres quat tu
s the loer urns on Her God / imothy C. akach solo n œnœ. œ œ œ œ œb n Qui dam o su it um ar c i cu lo rum se tem, se tem, du o, œ œ œ œ œ œ se tem, se tem, du o, b se tem, or erusal uroses only. Do t use, coy, or distribute. œ œ se tem, du o, œ œ. œbœ œ solo 1 œ œ œ in π œ œ œ œ. ze hy rum, œ œ ze hy rum, ze hy rum, vem, se tem, ze hy rum, ze hy rum, vem, se tem, œ œ quo dam lo co, qui er at n ze hy rum, π π vem, or erusal uroses only. Do t use, coy, or distribute. π œ œ œ nœ se tem, œ œ œ œ ze hy rum, ze hy rum, vem, se tem,
solo 5 s the loer urns on Her God / imothy C. akach ot. œ œ breath, ƒ ( ) œ œ n dim. di que ar i e te cir cum da t n dim. œ œ œ. ƒ vem, ze hy rum, quin n vem, b vem, ze hy rum,... œ vem, ze hy rum, œ. ze hy rum,.. ƒ quin que, n que, ƒ quin or erusal uroses only. Do t use, coy, or distribute. n dim. n dim. que, 0 h = 70 soli b. œ bœ b N œ œ b b se tem, du o, du o solo se tem, solo se tem, du o, du o solo b. œ œ du o,. b. œ œ œ œ œ œ du o œ œ or erusal uroses only. Do t use, coy, or distribute. œ œ b se tem, du o, du o 5
5 b. b œ œ s the loer urns on Her God / imothy C. akach b. quin que, quat tu. b b quat quat quat tu tu tu œ. du o, du o se tem, ze hy rum,.. or erusal uroses only. Do t use, coy, or distribute. œ œ solo 9 C tutti tutti tutti tutti ut Warmly h = 5 quin que, du o, quat tu du o, du o se tem, quat tu du o, du o se tem, œ. quat tu du o, du o se tem, sci ret, quot ex e o or erusal uroses only. Do t use, coy, or distribute. quat tu du o, du o se œ œ ze hy rum, quat tu œ œ œ œ tem,
s the loer urns on Her God / imothy C. akach solo 5 ze ze ar i a ger mi na ren tur hy rum, quin que, du o, hy rum, quin que, du o, ze ze hy rum, quin que, du o, du o, or erusal uroses only. Do t use, coy, or distribute. hy rum, quin que, du o, œ œ 55 vem... ze hy rum, du o, quat tu ze hy rum, quat tu ze hy rum, quat tu ze hy rum, quat tu π or erusal uroses only. Do t use, coy, or distribute. ze hy rum, quat tu œ. œ œ 7
s the loer urns on Her God / imothy C. akach 58 du o, du o, œ œ du o, quat tu vem, se tem, du o, or erusal uroses only. Do t use, coy, or distribute. solo 1 ritard U in o an or erusal uroses only. Do t use, coy, or distribute.. U U U U U 8
Revieed as gorgeous (Washington ost) and stning (Larence JournalWorld), the music o imothy C. akach has risen ast in the concert orld. lauded or his melodic lines and rich, intriguing harmonies, akach has received commissions rom the t. Ola and, Cant avia Winds, Lorelei Ensemble, alessence, the Deartolo erorming rts Center, he Rose Ensemble, and numerous other organizations. His comositions have been erormed on rairie Home Comanion, he oston os holiday tour, multile lltate and estival rograms and at venues such as the Library o Congress, Kennedy Center and Royal Oera House Muscat. He is a creator o the theatrical roduction o ll is Calm: the Christmas ruce o 191, by eter Rothstein. akach studied music comosition at t. Ola College, Northield, MN, here he graduated ith hors. He has requent national ork as a comoserinresidence, resenter, clinician and lecturer. He is a ulltime comoser and lives in Minneaolis ith his ie and to sons. elected val orks by imothy C. akach: Mixed oices Deth We Cant od, vibrahone, marimba, large tom Worshier and a Man a caella nd I a div. a caella s the loer urns on Her God div, o. solo, soli, a caella he Darkling hrush (earthsongs), soli, a caella ragile, hand drum Listen to the les div. a caella Neither ngels, Nor Demons, Nor oers (Grahite ublishing) a caella Nubes Oriebatur: the erution o esuvius a caella One oy old Me, ia u Rahva Koda (he House o Your Kindred) a caella his lien Landscae, crotales, susended cymbal, bass drum his mazing Lie (), ia We re Lost, We re Lucky, ia We ing o Home (inlandia) a caella reble oices Men s oices nd I a div. a caella Cassioeia a caella Goodbye, hen choir, b clarinet, ia Home on the Range (arr. merican olk ong) (Grahite ublishing) art treble, ia Queen o the Range (Grahite ublishing), ia erenade (Grahite ublishing) a caella he treets o Laredo (arr. merican olk ong) (Grahite ublishing) Unison,, ia here is No Rose (Lorelei Ensemble), soli, a caella orn Ma (Grahite ublishing), ia enty Questions art treble, ia Emty (ot. div), ia, ot. djembe Goodbye, hen choir, b clarinet, ia I Will Hol choir, ia or cello Kin, ia Luceat Eis a caella Mad, ia Original Harmony (Colla e) a caella Rough east (Jeremy D. Jones Male Choral eries), ercussion alve Regina (Grahite ublishing) semichor a caella hings I Didn t K I Loved (Grahite ublishing) a caella Large Works We Made a Grave or Him, nd Her moke Rose U orever (ca. 10 ) he Longest Nights (ca. 1 ) Where eauty Comes rom (ca. 1 ) a caella, ia or string quartet, art,, ; ia