{"text_format":"1","workbook":"xlsx","n_sheets":6,"sheets":["ChartData","WellChart","BigMajorChart","MeanChart","Panoply","Constants"],"not_rendered":{"charts":10,"images":1,"macros":1,"external_links":1,"defined_names":60,"comments":1,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900"}

{"sheet":"ChartData","index":0,"n_rows":77,"n_cols":28,"rows_kept":77,"cut":false,"hidden":false,"merged":[[75,0,75,2],[76,0,76,2],[71,0,71,2],[72,0,72,2],[73,0,73,2],[74,0,74,2]]}
["This Excel workbook is protected."]
["You can change only the offsets in the outlined-in-blue blue cells below, and green cells to the right."]
["The data (the twelve offsets and the title) are used in the \"Panoply\" sheet to calculate all the cents and beat rates."]
["The four mini-graphs change in real time as you modify the offsets."]
["They have larger versions with data on the two chart pages following."]
[]
[]
[]
[null,null,"Chart data",null,"Try these:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Enter your own experiments below:"]
[]
["Title of chart:",null,"Dr. Herbert Anton Kellner (Wohltemperirt/Bach, 1978)",null,"1/4 Syntonic Meantone","Barnes \"Bach\" (1979) - 1/6 PC","Bremmer's EBVT2","Coleman 11 (Modern Well, 1999)","Dr. Herbert Anton Kellner (Wohltemperirt/Bach, 1978)","EBVT III","Equal Beating Koval (EBK) (2002)","Francesco Antonio Vallotti (Well, 1781)","Roshan Kakiya's Well Temperament","Johann Philipp Kirnberger (Equal-Beating Well, 1771)","Koval Variable Well 1.5","Stanhope (Improved Kirnberger Equal-Beating Well, 1806)","Wendell Synchronous ET Equivalent, 2002","Werckmeister III (Well, 1691)","Roshan Kakiya's Practical Just Intonation (Alternative Tritone)","Actually you can enter your own data here in the green cells."]
["C  ",null,8.0990000000000002,null,10.264714601373726,5.87,3.8,3,8.0990000000000002,3.7979102391290032,3,5.8650000000000002,0,4.8547500000000001,1.5,11.091390000000001,2.74,11.73,0]
["C#",null,-1.6759999999999999,null,-13.686286135165574,0,-1.1000000000000001,0,-1.6759999999999999,-1.2851448079524228,0,0,1.96,-4.9202599999999999,-0.2,4.6944100000000004,-0.78,1.96,-1.05]
["D  ",null,2.8,null,3.4215715337916208,1.96,0.5,0,2.8,0.85687304330542025,0.5,1.9550000000000001,0,8.7647499999999994,0.5,4.8475000000000001,2.35,3.91,3.91]
["D#",null,2.2000000000000002,null,20.529429202747224,3.91,2.8,0,2.2000000000000002,1.5903590511483585,0.6,3.91,1.96,-1.0102599999999999,0.9,8.6044099999999997,1.17,5.87,-2.4900000000000002]
["E  ",null,-2.843,null,-3.4215715337913934,-1.96,0.6,-3,-2.843,-0.40624511383861756,-1.5,-1.9550000000000001,0,-8.8315400000000004,-0.6,-2.5948899999999999,1.96,1.96,4.4400000000000004]
["F  ",null,6.1,null,13.686286135164892,7.82,1.8,4,6.1,1.8426518307688871,2.5,7.82,1.96,2.89975,1.4,9.1363900000000005,0.78,9.7799999999999994,-1.96]
["F#",null,-3.6309999999999998,null,-10.26471460137418,-1.96,-2.1,-2,-3.6309999999999998,-0.28477571414974934,-1.5,-1.9550000000000001,0,-4.9215400000000002,-0.8,2.7394099999999999,1.56,0,3]
["G  ",null,5.5,null,6.8431430675823322,3.91,2.2000000000000002,2,5.5,3.1107326118845426,1.8,3.91,1.96,6.8097500000000002,1,13.046390000000001,0.39,7.82,1.96]
["G#",null,0.3,null,-17.107857668956512,1.96,0.8,0,0.3,0.66990389650368787,1.2,1.9550000000000001,0,-2.9652599999999998,0.4,6.6494099999999996,1.17,3.91,0.91]
["A  ",null,0,null,0,0,0,-1,0,0,0,0,1.96,0,0,0,0,0,5.87]
["A#",null,4.2,null,17.107857668956058,5.87,2.4,2,4.2,2.8552953850798062,1.7,5.8650000000000002,0,0.94474999999999998,1.25,7.1813900000000004,3.13,7.82,-3.91]
["B  ",null,-0.88800000000000001,null,-6.8431430675827869,0,-1.1000000000000001,-4,-0.88800000000000001,-2.7199792602806305E-2,-1.5,-3.91,1.96,-6.8765400000000003,-0.75,-0.63988999999999996,-0.39,3.91,1.05]
[]
[]
["This Excel workbook designed by Jason Kanter and used to create charts on rollingball.com"]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,"Smallest M3",{"$f":"ROUND(MIN(F38:F49),1)","v":2.7}]
[null,null,null,null,null,null,null,null,null,null,"Largest M3",{"$f":"ROUND(MAX(F38:F49),1)","v":21.5}]
["Below: Extracting chart data from Panoply."]
[]
["Major Triads",null,"SourceNotes","Tonic","Offset (cents)","M3 ¢ ","M3 bps","m3 ¢","m3 bps","5th ¢","5th bps"]
["CEG",null,"C3-E3-G3",{"$f":"LEFT(A38,1)","v":"C"},{"$f":"cee","v":8.0990000000000002},{"$f":"Panoply!G64","v":2.7442861351655967},{"$f":"Panoply!H64","v":1.0424848576599288},{"$f":"Panoply!J60","v":-7.2982870005527714},{"$f":"Panoply!K60","v":-4.1531884003588857},{"$f":"Panoply!M64","v":-4.554000865386838},{"$f":"Panoply!N64","v":-1.0357844455475629}]
["GBD",null,"G3-B3-D4",{"$f":"LEFT(A39,1)","v":"G"},{"$f":"gee","v":5.5},{"$f":"Panoply!G57","v":7.2982861351655677},{"$f":"Panoply!H57","v":4.1531879068598982},{"$f":"Panoply!J53","v":-11.953287000552114},{"$f":"Panoply!K53","v":-10.189572622040941},{"$f":"Panoply!M57","v":-4.6550008653865147},{"$f":"Panoply!N57","v":-1.5839163047004376}]
["DF#A",null,"D3-F#3-A3","D",{"$f":"dee","v":2.8},{"$f":"Panoply!G62","v":7.2552861351654121},{"$f":"Panoply!H62","v":3.0881853603915488},{"$f":"Panoply!J58","v":-12.010287000552198},{"$f":"Panoply!K58","v":-7.6576867498224601},{"$f":"Panoply!M62","v":-4.7550008653868998},{"$f":"Panoply!N62","v":-1.2101634836940889}]
["AC#E",null,"A3-C#4-E4","A",{"$f":"aaa","v":0},{"$f":"Panoply!G55","v":12.010286135165495},{"$f":"Panoply!H55","v":7.6576861961409577},{"$f":"Panoply!J51","v":-16.808287000551882},{"$f":"Panoply!K51","v":-16.053064507613271},{"$f":"Panoply!M55","v":-4.7980008653862924},{"$f":"Panoply!N55","v":-1.8266140853606885}]
["EG#B",null,"E3-G#3-B3","E",{"$f":"eee","v":-2.843},{"$f":"Panoply!G60","v":16.829286135165443},{"$f":"Panoply!H60","v":8.0366088783121086},{"$f":"Panoply!J56","v":-16.829287000552611},{"$f":"Panoply!K56","v":-12.054913934341812},{"$f":"Panoply!M60","v":-8.6538721848522665E-7},{"$f":"Panoply!N60","v":-2.4674949372638366E-7}]
["BD#F#",null,"B3-D#4-F#4","B",{"$f":"bee","v":-0.88800000000000001},{"$f":"Panoply!G53","v":16.774286135165937},{"$f":"Panoply!H53","v":12.015325329689176},{"$f":"Panoply!J49","v":-21.472287000552463},{"$f":"Panoply!K49","v":-23.03949037110624},{"$f":"Panoply!M53","v":-4.6980008653866063},{"$f":"Panoply!N53","v":-2.006600950628922}]
["F#A#C#",null,"F#3-A#3-C#4",{"$f":"LEFT(A44,2)","v":"F#"},{"$f":"fsharp","v":-3.6309999999999998},{"$f":"Panoply!G58","v":21.517286135165563},{"$f":"Panoply!H58","v":11.544037273387971},{"$f":"Panoply!J54","v":-21.517287000552081},{"$f":"Panoply!K54","v":-17.316056602183835},{"$f":"Panoply!M58","v":-8.6538664186845572E-7},{"$f":"Panoply!N58","v":-2.7684075121214846E-7}]
["C#FG#",null,"C#3-F3-G#3",{"$f":"LEFT(A45,2)","v":"C#"},{"$f":"csharp","v":-1.6759999999999999},{"$f":"Panoply!G63","v":21.462286135164863},{"$f":"Panoply!H63","v":8.6357598396249386},{"$f":"Panoply!J59","v":-21.441287000552116},{"$f":"Panoply!K59","v":-12.941043978805965},{"$f":"Panoply!M63","v":2.0999134612990474E-2},{"$f":"Panoply!N63","v":5.0383122526227453E-3}]
["AbCEb",null,"Ab3-C4-Eb4",{"$f":"LEFT(A46,2)","v":"Ab"},{"$f":"aflat","v":0.3},{"$f":"Panoply!G56","v":21.485286135165317},{"$f":"Panoply!H56","v":12.967765101653413},{"$f":"Panoply!J52","v":-21.540287000551725},{"$f":"Panoply!K52","v":-19.501133408296027},{"$f":"Panoply!M56","v":-5.5000865386661532E-2},{"$f":"Panoply!N56","v":-1.9794302326317847E-2}]
["EbGBb",null,"Eb3-G3-Bb3",{"$f":"LEFT(A47,2)","v":"Eb"},{"$f":"eflat","v":2.2000000000000002},{"$f":"Panoply!G61","v":16.986286135165365},{"$f":"Panoply!H61","v":7.678997813052888},{"$f":"Panoply!J57","v":-16.941287000552229},{"$f":"Panoply!K57","v":-11.488131609785569},{"$f":"Panoply!M61","v":4.4999134612723299E-2},{"$f":"Panoply!N61","v":1.2146043917425686E-2}]
["BbDF",null,"Bb3-D4-F4",{"$f":"LEFT(A48,2)","v":"Bb"},{"$f":"bflat","v":4.2},{"$f":"Panoply!G54","v":12.28628613516565},{"$f":"Panoply!H54","v":8.3202990003846935},{"$f":"Panoply!J50","v":-12.341287000552148},{"$f":"Panoply!K50","v":-12.536119654243976},{"$f":"Panoply!M54","v":-5.5000865386469318E-2},{"$f":"Panoply!N54","v":-2.2268461466751432E-2}]
["FAC",null,"F3-A3-C4","F",{"$f":"eff","v":6.1},{"$f":"Panoply!G59","v":7.5862861351655582},{"$f":"Panoply!H59","v":3.8477328597339238},{"$f":"Panoply!J55","v":-7.5422870005525713},{"$f":"Panoply!K55","v":-5.7381978860416893},{"$f":"Panoply!M59","v":4.3999134613262755E-2},{"$f":"Panoply!N59","v":1.3360561423723993E-2}]
["CEG",null,"C4-E4-G4","C",{"$f":"cee","v":8.0990000000000002},{"$f":"Panoply!G52","v":2.7442861351663637},{"$f":"Panoply!H52","v":2.0849697153203124},{"$f":"Panoply!J48","v":-7.2982870005525768},{"$f":"Panoply!K48","v":-8.3063768007177714},{"$f":"Panoply!M52","v":-4.5540008653866453},{"$f":"Panoply!N52","v":-2.0715688910950121}]
[]
[]
["Minor Triads",null,"SourceNotes","Tonic","Offset (cents)","M3 ¢ ","M3 bps","m3 ¢","m3 bps","5th ¢","5th bps"]
["CEbG",null,"C3-Eb3-G3",{"$f":"D38","v":"C"},{"$f":"cee","v":8.0990000000000002},{"$f":"F47","v":16.986286135165365},7.678997813052888,{"$f":"Panoply!J64","v":-21.540287000552116},{"$f":"Panoply!K64","v":-9.7505667041480137},{"$f":"J38","v":-4.554000865386838},-1.0357844455475629]
["GBbD",null,"G3-Bb3-D4",{"$f":"D39","v":"G"},{"$f":"gee","v":5.5},12.28628613516565,8.3202990003846935,{"$f":"H47","v":-16.941287000552229},{"$f":"I47","v":-11.488131609785569},-4.6550008653865147,-1.5839163047004376]
["DFA",null,"D3-F3-A3","D",{"$f":"dee","v":2.8},7.5862861351655582,3.8477328597339238,{"$f":"H48","v":-12.341287000552148},{"$f":"I48/2","v":-6.2680598271219878},-4.7550008653868998,-1.2101634836940889]
["ACE",null,"A3-C4-E4","A",{"$f":"aaa","v":0},2.7442861351663637,2.0849697153203124,-7.5422870005525713,-5.7381978860416893,-4.7980008653862924,-1.8266140853606885]
["EGB",null,"E3-G3-B3","E",{"$f":"eee","v":-2.843},{"$f":"F39","v":7.2982861351655677},{"$f":"G39","v":4.1531879068598982},-7.2982870005525768,{"$f":"I50/2","v":-4.1531884003588857},-8.6538721848522665E-7,-2.4674949372638366E-7]
["BDF#",null,"B3-D4-F#4","B",{"$f":"bee","v":-0.88800000000000001},{"$f":"F40","v":7.2552861351654121},{"$f":"G40*2","v":6.1763707207830976},{"$f":"H39","v":-11.953287000552114},{"$f":"I39","v":-10.189572622040941},-4.6980008653866063,-2.006600950628922]
["F#AC#",null,"F#3-A3-C#4","F#",{"$f":"fsharp","v":-3.6309999999999998},12.010286135165495,7.6576861961409577,{"$f":"H40","v":-12.010287000552198},-7.6576867498224601,-8.6538664186845572E-7,-2.7684075121214846E-7]
["C#EG#",null,"C#3-E3-G#3","C#",{"$f":"csharp","v":-1.6759999999999999},16.829286135165443,8.0366088783121086,-16.808287000551882,{"$f":"I41/2","v":-8.0265322538066357},2.0999134612990474E-2,5.0383122526227453E-3]
["AbBEb",null,"Ab3-B3-Eb4","Ab",{"$f":"aflat","v":0.3},16.774286135165937,12.015325329689176,-16.829287000552611,-12.054913934341812,-5.5000865386661532E-2,-1.9794302326317847E-2]
["EbGbBb",null,"Eb3-Gb3-Bb3","Eb",{"$f":"eflat","v":2.2000000000000002},21.517286135165563,11.544037273387971,-21.472287000552463,{"$f":"I43/2","v":-11.51974518555312},4.4999134612723299E-2,1.2146043917425686E-2]
["BbDbF",null,"Bb3-Db4-F4","Bb",{"$f":"bflat","v":4.2},21.462286135164863,{"$f":"G45*2","v":17.271519679249877},-21.517287000552081,-17.316056602183835,-5.5000865386469318E-2,-2.2268461466751432E-2]
["FAbC",null,"F3-Ab3-C4","F",{"$f":"eff","v":6.1},21.485286135165317,12.967765101653413,-21.441287000552116,-12.941043978805965,4.3999134613262755E-2,1.3360561423723993E-2]
["CEbG",null,"C4-Eb4-G4","C",{"$f":"cee","v":8.0990000000000002},16.986286135165365,{"$f":"G47*2","v":15.357995626105776},-21.540287000551725,-19.501133408296027,-4.5540008653866453,-2.0715688910950121]
[]
[]
[]
["Rearranging chart data for easier linking."]
["MAJOR",null,null,"C Maj",null,"G Maj",null,"D Maj",null,"A Maj",null,"E Maj",null,"B Maj",null,"F# Maj",null,"C# Maj",null,"Ab Maj",null,"Eb Maj",null,"Bb Maj",null,"F Maj",null,"C Maj"]
["M3 ¢",null,null,{"$f":"F38","v":2.7442861351655967},null,{"$f":"F39","v":7.2982861351655677},null,{"$f":"F40","v":7.2552861351654121},null,{"$f":"F41","v":12.010286135165495},null,{"$f":"F42","v":16.829286135165443},null,{"$f":"F43","v":16.774286135165937},null,{"$f":"F44","v":21.517286135165563},null,{"$f":"F45","v":21.462286135164863},null,{"$f":"F46","v":21.485286135165317},null,{"$f":"F47","v":16.986286135165365},null,{"$f":"F48","v":12.28628613516565},null,{"$f":"F49","v":7.5862861351655582},null,{"$f":"F50","v":2.7442861351663637}]
["m3 ¢",null,null,{"$f":"H38","v":-7.2982870005527714},null,{"$f":"H39","v":-11.953287000552114},null,{"$f":"H40","v":-12.010287000552198},null,{"$f":"H41","v":-16.808287000551882},null,{"$f":"H42","v":-16.829287000552611},null,{"$f":"H43","v":-21.472287000552463},null,{"$f":"H44","v":-21.517287000552081},null,{"$f":"H45","v":-21.441287000552116},null,{"$f":"H46","v":-21.540287000551725},null,{"$f":"H47","v":-16.941287000552229},null,{"$f":"H48","v":-12.341287000552148},null,{"$f":"H49","v":-7.5422870005525713},null,{"$f":"H50","v":-7.2982870005525768}]
["5th ¢",null,null,{"$f":"J38","v":-4.554000865386838},null,{"$f":"J39","v":-4.6550008653865147},null,{"$f":"J40","v":-4.7550008653868998},null,{"$f":"J41","v":-4.7980008653862924},null,{"$f":"J42","v":-8.6538721848522665E-7},null,{"$f":"J43","v":-4.6980008653866063},null,{"$f":"J44","v":-8.6538664186845572E-7},null,{"$f":"J45","v":2.0999134612990474E-2},null,{"$f":"J46","v":-5.5000865386661532E-2},null,{"$f":"J47","v":4.4999134612723299E-2},null,{"$f":"J48","v":-5.5000865386469318E-2},null,{"$f":"J49","v":4.3999134613262755E-2},null,{"$f":"J50","v":-4.5540008653866453}]
["M3 bps",null,null,{"$f":"G38","v":1.0424848576599288},null,{"$f":"G39","v":4.1531879068598982},null,{"$f":"G40","v":3.0881853603915488},null,{"$f":"G41","v":7.6576861961409577},null,{"$f":"G42","v":8.0366088783121086},null,{"$f":"G43","v":12.015325329689176},null,{"$f":"G44","v":11.544037273387971},null,{"$f":"G45","v":8.6357598396249386},null,{"$f":"G46","v":12.967765101653413},null,{"$f":"G47","v":7.678997813052888},null,{"$f":"G48","v":8.3202990003846935},null,{"$f":"G49","v":3.8477328597339238},null,{"$f":"G50","v":2.0849697153203124}]
["m3 bps",null,null,{"$f":"I38","v":-4.1531884003588857},null,{"$f":"I39","v":-10.189572622040941},null,{"$f":"I40","v":-7.6576867498224601},null,{"$f":"I41","v":-16.053064507613271},null,{"$f":"I42","v":-12.054913934341812},null,{"$f":"I43","v":-23.03949037110624},null,{"$f":"I44","v":-17.316056602183835},null,{"$f":"I45","v":-12.941043978805965},null,{"$f":"I46","v":-19.501133408296027},null,{"$f":"I47","v":-11.488131609785569},null,{"$f":"I48","v":-12.536119654243976},null,{"$f":"I49","v":-5.7381978860416893},null,{"$f":"I50","v":-8.3063768007177714}]
["5th bps",null,null,{"$f":"K38","v":-1.0357844455475629},null,{"$f":"K39","v":-1.5839163047004376},null,{"$f":"K40","v":-1.2101634836940889},null,{"$f":"K41","v":-1.8266140853606885},null,{"$f":"K42","v":-2.4674949372638366E-7},null,{"$f":"K43","v":-2.006600950628922},null,{"$f":"K44","v":-2.7684075121214846E-7},null,{"$f":"K45","v":5.0383122526227453E-3},null,{"$f":"K46","v":-1.9794302326317847E-2},null,{"$f":"K47","v":1.2146043917425686E-2},null,{"$f":"K48","v":-2.2268461466751432E-2},null,{"$f":"K49","v":1.3360561423723993E-2},null,{"$f":"K50","v":-2.0715688910950121}]

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["MAJOR TRIADS",null,null,"Triads arranged around the circle of fifths.\nVertical scale of +/- 25 cents - adequate for all but meantone temperaments.\nRed = M3. Blue = Fifth. Green = m3.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"minor triads",null,null,"Columns represents cents away from just. \nNumbers represent beats per second in region C3-C4."]
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[null,"Major Triads",null,"cents",{"$f":"commentary","v":0}]
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["MAJOR TRIADS",null,null,"Triads arranged around the circle of fifths.\nVertical scale of +50 to -55 cents - good for displaying meantone temperaments.\nRed = M3. Blue = Fifth. Green = m3.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"minor triads",null,null,"Columns represents cents away from just. \nNumbers represent beats per second in region C3-C4."]
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{"sheet":"Panoply","index":4,"n_rows":91,"n_cols":20,"rows_kept":91,"cut":false,"hidden":false,"merged":[[2,0,2,1]]}
["This sheet does not include any inharmonicity calculations. ",null,"We build an \"ET\" scale up and down from A4=440","The ET will be modified by the twelve offsets in the ChartData sheet","The corrected fundamental is calculated by '=fundamental*\n(cent^offset)","The Just M3 is the basis for assessing the sizes of the M3","Size in cents of the M3 on this note","Beats of the 5th partial of the lower vs the 4th partial of the upper","The Just m3 is the basis for assessing the sizes of the m3","Size in cents of the m3 on this note","Beats of the 6th partial of the lower vs the 5th partial of the upper","The Just 5th is the basis for assessing the sizes of the fifths","Size in cents of the 5th on this note","Beats of the 3rd partial of the lower vs the 2nd partial of the upper","The Just 4th is the basis for assessing the sizes of the fourths","Size in cents of the 4th on this note","Beats of the 4th partial of the lower vs the 3rd partial of the upper","The Just M6 is the basis for assessing the sizes of the M6","Size in cents of the M6 on this note","Beats of the 5th partial of the lower vs the 3rd partial of the upper"]
[null,null,null,null,"name: cfund","=(5/4)*cfund",null,null,"=(6/5)*cfund",null,null,"=(3/2)*cfund",null,null,"=(4/3)*cfund",null,null,"=(5/3)*cfund"]
["Note",null,"Fundamental (ET)","offsets","Corrected fund","Just M3","M3c","M3b","Just m3","m3c","m3b","Just 5th","5c","5b","Just 4th","4c","4b","Just M6","M6c","M6b"]
["C",8,{"$f":"C5*semitone","v":4186.0090448095834},{"$f":"cee","v":8.0990000000000002},{"$f":"fundamental*(cent^offset)","v":4205.6377667646711}]
["B",7,3951.066410048998,{"$f":"bee","v":-0.88800000000000001},3949.0403135138417]
["A#",7,3729.310092144724,{"$f":"asharp","v":4.2},3738.3684382596316]
["A",7,3520.0000000000041,{"$f":"aaa","v":0},3520.0000000000041,null,null,null,{"$f":"(6/5)*E7","v":4224.0000000000045},{"$f":"1200*(LOG($E4/I7)/LOG(octave))","v":-7.5422870005525713},{"$f":"5*$E4-6*$E7","v":-91.811166176670667}]
["G#",7,3322.4375806395647,{"$f":"gsharp","v":0.3},3323.0133650864464,{"$f":"E8*1.25","v":4153.7667063580575},{"$f":"1200*(LOG($E4/F8)/LOG(octave))","v":21.485286135165317},{"$f":"4*$E4-5*$E8","v":207.4842416264546},{"$f":"(6/5)*E8","v":3987.6160381037353},-16.829287000552224,{"$f":"5*$E5-6*$E8","v":-192.87862294946899}]
["G",7,3135.9634878539978,{"$f":"gee","v":5.5},3145.9420495091217,3932.4275618864021,{"$f":"1200*(LOG(E5/F9)/LOG(octave))","v":7.2982861351655677},{"$f":"4*E5-5*E9","v":66.451006509758372},3775.1304594109461,-16.941287000552425,-183.81010575657274,null,null,null,{"$f":"(4/3)*cfund","v":4194.5893993454956},{"$f":"1200*(LOG($E4/O9)/LOG(octave))","v":4.5540008653874011},{"$f":"3*$E4-4*$E9","v":33.145102257527469}]
["F#",7,2959.9553816930784,{"$f":"fsharp","v":-3.6309999999999998},2953.7538313328637,3692.1922891660797,21.517286135165563,184.70459637420754,3544.5045975994362,-12.010287000552198,-122.52298799715936,null,null,null,3938.3384417771513,4.6980008653878071,{"$f":"3*$E5-4*$E10","v":32.105615210070027}]
["F",7,2793.8258514640338,{"$f":"eff","v":6.1},2803.6872548488545,3504.6090685610679,7.586286135165941,61.563725755744599,3364.4247058186252,-21.441287000552116,-207.05670366089907,{"$f":"(3/2)*E11","v":4205.5308822732823},{"$f":"1200*(LOG($E4/L11)/LOG(octave))","v":4.3999134612878354E-2},{"$f":"2*$E4-3*$E11","v":0.2137689827777649},3738.249673131806,5.5000865387819953E-2,0.35629538347711787]
["E",7,2637.0204553029621,{"$f":"eee","v":-2.843},2632.6935436585586,3290.8669295731984,16.829286135165063,128.58574205299192,3159.2322523902703,-7.2982870005527714,-66.451014405742171,{"$f":"(3/2)*E12","v":3949.0403154878377},-8.6538721848522665E-7,{"$f":"2*$E5-3*$E12","v":-3.9479918996221386E-6},3510.2580582114115,4.7980008653876078,29.225825365778292]
["D#",7,2489.0158697766497,{"$f":"dsharp","v":2.2000000000000002},2492.1808466055281,3115.2260582569102,16.986286135165365,122.86396500884621,2990.6170159266335,-21.472287000552463,-184.31592296884992,3738.2712699082922,4.4999134612723299E-2,{"$f":"2*$E6-3*$E13","v":0.19433670267881098},3322.9077954740374,5.5000865387819953E-2,0.31670883722654253,{"$f":"(5/3)*E13","v":4153.6347443425475},{"$f":"1200*(LOG($E4/R13)/LOG(octave))","v":21.540287000552304},{"$f":"3*$E4-5*$E13","v":156.00906726637368}]
["D",7,2349.3181433392624,{"$f":"dee","v":2.8},2353.1208719130377,2941.401089891297,7.255286135165794,49.4109657662666,2823.7450462956454,-12.341287000552535,-100.28895723395544,3529.6813078695568,-4.7550008653868998,-19.362615739105422,3137.4944958840501,4.6550008653877919,25.342660875214278,{"$f":"(5/3)*E14","v":3921.868119855063},11.953287000553207,{"$f":"3*$E5-5*$E14","v":81.516580976336627}]
["C#",7,2217.4610478149784,{"$f":"csharp","v":-1.6759999999999999},2215.3153723922833,2769.1442154903543,21.462286135165247,138.17215743400084,2658.3784468707399,-16.808287000551882,-128.42451606090617,3322.9730585884249,2.0999134613374878E-2,8.0612996042873419E-2,2953.7538298563777,8.6538798687500838E-7,4.429457476362586E-6,3692.1922873204721,21.517287000553349,138.52845281747796]
["C",7,2093.0045224047904,{"$f":"D4","v":8.0990000000000002},2102.8188833823342,2628.5236042279175,2.7442861351663637,16.679757722564318,2523.3826600588009,-21.540287000551533,-156.00906726636458,3154.2283250735013,-4.5540008653862598,-16.572551128759187,2803.7585111764456,-4.3999134611708568E-2,-0.21376898277230794,3504.698138970557,7.5422870005538876,45.90558308834261]
["B",6,1975.5332050244976,{"$f":"D5","v":-0.88800000000000001},1974.5201567569195,2468.1501959461493,16.774286135165937,96.122602637515229,2369.4241881083035,-11.953287000552114,-81.516580976329351,2961.7802351353794,-4.6980008653866063,-16.052807605031376,2632.6935423425593,8.6538837128618868E-7,3.9479973565903492E-6,3290.8669279281994,16.829287000553574,96.439311474741771]
["A#",6,1864.6550460723606,4.2,1869.1842191298144,2336.4802739122679,12.28628613516603,66.562392003079367,2243.0210629557773,-21.517287000552081,-138.52845281746886,2803.7763286947215,-5.5000865386469318E-2,-0.17814769173401146,2492.2456255064189,-4.4999134611470287E-2,-0.19433670267335401,3115.3070318830241,16.941287000553519,91.905052878293645]
["A",6,1760.0000000000009,0,1760.0000000000009,2200.0000000000009,12.010286135165877,61.261489569129481,2112.0000000000009,-7.5422870005525713,-45.905583088335334,2640.0000000000014,-4.7980008653862924,-14.612912682885508,2346.6666666666679,4.7550008653879354,19.36261573910997,2933.3333333333348,12.010287000553546,61.261493998586957]
["G#",6,1661.2187903197814,0.3,1661.5066825432223,2076.8833531790278,21.485286135164934,103.74212081322548,1993.8080190518667,-16.829287000552611,-96.439311474736314,2492.2600238148334,-5.5000865386661532E-2,-0.15835441861054278,2215.3422433909627,-2.0999134611968336E-2,-8.0612996039235441E-2,2769.1778042387041,21.441287000552972,103.52835183045318]
["G",6,1567.981743926998,5.5,1572.9710247545599,1966.2137809431999,7.2982861351651849,33.225503254878276,1887.5652297054719,-16.941287000552617,-91.905052878288188,2359.4565371318399,-4.6550008653869011,-12.671330437604411,2097.2946996727464,4.5540008653874011,16.572551128762825,2621.6183745909334,7.2982870005538114,33.225507202875633]
["F#",6,1479.9776908465383,-3.6309999999999998,1476.8769156664309,1846.0961445830387,21.517286135165179,92.352298187102861,1772.252298799717,-12.010287000552198,-61.2614939985815,2215.3153734996463,-8.6538664186845572E-7,-2.2147260096971877E-6,1969.1692208885745,4.6980008653878071,16.052807605035014,2461.4615261107183,21.472287000553695,92.157961484429507]
["F",6,1396.9129257320162,6.1,1401.8436274244266,1752.3045342805333,7.5862861351651762,30.781862877870481,1682.2123529093119,-21.441287000552315,-103.52835183044772,2102.7654411366398,4.3999134612878354E-2,0.10688449138888245,1869.1248365659021,5.5000865387435545E-2,0.17814769173673994,2336.4060457073779,12.341287000553264,50.14447861698045]
["E",6,1318.5102276514804,-2.843,1316.3467718292786,1645.4334647865983,16.829286135165063,64.292871026495959,1579.6161261951343,-7.2982870005527714,-33.225507202871995,1974.5201577439179,-8.6538760289640727E-7,-1.9739968593057711E-6,1755.1290291057048,4.7980008653872241,14.612912682888236,2193.911286382131,16.808287000552916,64.212258030456724]
["D#",6,1244.5079348883241,2.2000000000000002,1246.0904233027634,1557.6130291284542,16.986286135165365,61.431982504423104,1495.3085079633161,-21.472287000552654,-92.157961484425869,1869.1356349541452,4.4999134612338891E-2,9.7168351338495995E-2,1661.4538977370178,5.5000865387819953E-2,0.15835441861327126,2076.8173721712724,21.540287000552304,78.004533633185929]
["D",6,1174.6590716696307,2.8,1176.5604359565184,1470.7005449456481,7.2552861351650293,24.705482883131481,1411.872523147822,-12.341287000552535,-50.144478616976812,1764.8406539347775,-4.7550008653870917,-9.6813078695531658,1568.7472479420244,4.6550008653877919,12.67133043760623,1960.9340599275308,11.953287000552441,40.758290488166494]
["C#",6,1108.7305239074888,-1.6759999999999999,1107.6576861961412,1384.5721077451765,21.462286135165247,69.086078717000419,1329.1892234353693,-16.808287000551882,-64.212258030453995,1661.4865292942118,2.0999134612990474E-2,4.0306498020981962E-2,1476.8769149281882,8.6538760246382807E-7,2.2147278286865912E-6,1846.0961436602354,21.517287000552585,69.264226408737159]
["C",6,1046.5022612023949,8.0990000000000002,1051.4094416911669,1314.2618021139585,2.74428613516598,8.3398788612803401,1261.6913300294002,-21.540287000552116,-78.004533633185019,1577.1141625367504,-4.5540008653870307,-8.2862755643809578,1401.8792555882223,-4.3999134612092983E-2,-0.10688449138797296,1752.3490694852783,7.5422870005531228,22.952791544168576]
["B",5,987.7666025122486,-0.88800000000000001,987.26007837845953,1234.0750979730744,16.774286135165561,48.061301318755795,1184.7120940541513,-11.953287000552114,-40.758290488164675,1480.8901175676892,-4.6980008653871845,-8.0264038025165974,1316.3467711712792,8.6538837128618868E-7,1.9739977688004728E-6,1645.4334639640992,16.829287000553194,48.219655737369067]
["A#",5,932.3275230361802,4.2,934.5921095649071,1168.2401369561339,12.286286135165268,33.281196001537865,1121.5105314778884,-21.517287000552475,-69.264226408736249,1401.8881643473605,-5.5000865387045961E-2,-8.9073845867915225E-2,1246.1228127532095,-4.4999134612431338E-2,-9.7168351338041248E-2,1557.6535159415118,16.941287000552759,45.952526439144094]
["A",5,880.00000000000034,0,880.00000000000034,1100.0000000000005,12.010286135165115,30.630744784562921,1056.0000000000005,-7.5422870005529576,-22.952791544167667,1320.0000000000005,-4.7980008653870625,-7.3064563414436634,1173.3333333333337,4.7550008653875508,9.6813078695536205,1466.6666666666672,12.010287000552783,30.63074699929075]
["G#",5,830.6093951598906,0.3,830.75334127161102,1038.4416765895137,21.485286135164934,51.871060406612742,996.90400952593313,-16.829287000552611,-48.219655737368157,1246.1300119074165,-5.5000865387238175E-2,-7.9177209306180885E-2,1107.6711216954814,-2.0999134612737169E-2,-4.0306498020527215E-2,1384.5889021193518,21.441287000552588,51.764175915224769]
["G",5,783.99087196349888,5.5,786.48551237727986,983.10689047159985,7.2982861351651849,16.612751627438683,943.78261485273583,-16.941287000552617,-45.952526439143185,1179.7282685659197,-4.6550008653870929,-6.3356652188026601,1048.647349836373,4.5540008653874011,8.2862755643814126,1310.8091872954665,7.2982870005530449,16.612753601436452]
["F#",5,739.98884542326903,-3.6309999999999998,738.43845783321535,923.04807229151925,21.517286135165179,46.17614909355143,886.12614939985838,-12.010287000552198,-30.63074699928984,1107.6576867498229,-8.6538702627963634E-7,-1.1073634595959447E-6,984.58461044428714,4.6980008653874243,8.0264038025170521,1230.7307630553589,21.472287000552935,46.078980742213389]
["F",5,698.456462866008,6.1,700.92181371221318,876.15226714026653,7.5862861351651762,15.39093143893524,841.10617645465584,-21.441287000552315,-51.764175915223859,1051.3827205683197,4.3999134612878354E-2,5.3442245694441226E-2,934.56241828295083,5.5000865387819953E-2,8.9073845868369972E-2,1168.2030228536887,12.341287000552882,25.072239308488861]
["E",5,659.25511382574007,-2.843,{"$f":"fundamental*(cent^offset)","v":658.1733859146392},822.71673239329903,16.829286135165063,32.14643551324798,789.80806309756701,-7.2982870005527714,-16.612753601435543,987.26007887195874,-8.6538760289640727E-7,-9.8699842965288553E-7,877.56451455285219,4.7980008653876078,7.3064563414441182,1096.9556431910653,16.808287000552536,32.106129015227452]
["D#",5,622.25396744416196,2.2000000000000002,623.04521165138158,778.80651456422697,16.986286135165365,30.715991252211552,747.65425398165792,-21.472287000552654,-46.07898074221248,934.56781747707237,4.4999134612723299E-2,4.8584175669475371E-2,830.72694886850877,5.5000865387819953E-2,7.9177209306635632E-2,1038.408686085636,21.540287000552304,39.002266816592964]
["D",5,587.32953583481526,2.8,588.28021797825909,735.35027247282392,7.2552861351650293,12.35274144156574,705.93626157391088,-12.341287000552535,-25.072239308488406,882.42032696738863,-4.7550008653870917,-4.8406539347765829,784.37362397101208,4.6550008653877919,6.3356652188031148,980.46702996376519,11.953287000552441,20.379145244082792]
["C#",5,554.36526195374427,-1.6759999999999999,553.82884309807048,692.28605387258813,21.462286135165247,34.543039358500209,664.59461171768453,{"$f":"1200*(LOG($E36/I39)/LOG(octave))","v":-16.808287000551882},-32.106129015226543,830.74326464710566,2.0999134613374878E-2,2.0153249010718355E-2,738.43845746409397,8.6538760246382807E-7,1.1073639143432956E-6,923.04807183011746,21.517287000552969,34.632113204368579]
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["A",1,54.999999999999901,0,54.999999999999901,68.749999999999872,12.010286135165495,1.9144215490352394,65.999999999999872,-7.5422870005525713,-1.4345494715104792,82.499999999999858,-4.7980008653870625,-0.45665352134022896,73.333333333333201,4.7550008653875508,0.60508174184712971,91.666666666666501,12.010287000553166,1.9144216874557856]
["G#",1,51.913087197493049,0.3,51.922083829475575,64.902604786844464,21.485286135164934,3.2419412754132964,62.306500595370686,-16.829287000552807,-3.0137284835855098,77.883125744213359,-5.5000865387045961E-2,-4.9485755816078836E-3,69.229445105967429,-2.0999134612352751E-2,-2.5191561262545292E-3,86.536806382459289,21.441287000552972,3.2352609947016049]
["G",1,48.999429497718573,{"$f":"D69","v":5.5},49.155344523579885,61.444180654474856,7.2982861351651849,1.0382969767149177,58.986413428295862,-16.941287000552617,-2.8720329024465059,73.733016785369827,-4.6550008653870929,-0.39597907617516626,65.54045936477317,4.5540008653874011,0.51789222277380986,81.925574205966484,7.2982870005530449,1.0382971000898067]
["F#",1,46.249302838954215,-3.6309999999999998,46.15240361457586,57.690504518219825,21.517286135165179,2.8860093183469644,55.382884337491028,-12.010287000552198,-1.9144216874556719,69.22860542186379,-8.6538702627963634E-7,-6.9210216224746546E-8,61.536538152767811,4.6980008653874243,0.50165023765731576,76.920672690959776,21.472287000552935,2.8799362963883652]
["F",1,43.6535289291254,6.1,43.807613357013224,54.75951669626653,7.5862861351655582,0.96193321493348094,52.569136028415869,-21.441287000552116,-3.2352609947014912,65.711420035519836,4.3999134612878354E-2,3.3401403559025766E-3,58.410151142684299,5.5000865387819953E-2,5.567115366801545E-3,73.012688928355374,12.341287000553264,1.5670149567806106]
["E",1,41.203444614108662,-2.843,41.135836619664857,51.419795774581075,16.829286135165063,2.0091522195779987,49.363003943597825,-7.2982870005525768,-1.0382971000897214,61.703754929497286,-8.6538760289640727E-7,-6.1687401853305346E-8,54.847782159553141,4.7980008653876078,0.45665352134028581,68.559727699441439,16.808287000552536,2.0066330634517442]
["D#",1,38.890872965260037,2.2000000000000002,38.940325728211263,48.675407160264079,16.986286135165365,1.919749453263222,46.728390873853513,-21.472287000552463,-2.87993629638828,58.410488592316895,4.4999134612723299E-2,3.0365109793422107E-3,51.920434304281684,5.5000865387819953E-2,4.948575581664727E-3,64.900542880352106,21.540287000552681,2.4376416760370319]
["D",1,36.708095989675869,2.8,36.767513623641108,45.959392029551381,7.255286135165794,0.77204634009791562,44.121016348369331,-12.341287000552535,-1.5670149567805254,55.151270435461662,-4.7550008653868998,-0.30254087092352222,49.023351498188141,4.6550008653877919,0.3959790761752231,61.279189372735182,11.953287000552823,1.2736965777552314]
["C#",1,34.647828872108938,-1.6759999999999999,34.614302693629327,43.267878367036658,21.462286135165247,2.1589399599062631,41.537163232355191,-16.808287000551882,-2.0066330634516589,51.92145404044399,2.0999134613374878E-2,1.2595780631698972E-3,46.152403591505767,8.6538798687500838E-7,6.9210273068165407E-8,57.690504489382214,21.517287000552969,2.1645070752730646]
["C",1,32.703195662574757,8.0990000000000002,32.85654505284888,41.070681316061098,2.7442861351663637,0.26062121441503905,39.427854063418657,-21.54028700055192,-2.437641676036975,49.284817579273323,-4.5540008653866453,-0.25894611138687651,43.808726737131835,-4.3999134611708568E-2,-3.3401403558457332E-3,54.760908421414804,7.5422870005535048,0.71727473575532485]
["B",0,30.867706328507687,-0.88800000000000001,30.851877449326778,38.56484681165847,16.774286135165937,1.5019156662111754,37.022252939192136,-11.953287000552114,-1.2736965777551461,46.277816173990168,-4.6980008653866063,-0.25082511882861525,41.135836599102369,8.6538837128618868E-7,6.1687458696724207E-8,51.419795748877966,16.829287000553574,1.5068642417928402]
["A#",0,29.135235094880553,4.2,29.206003423903269,36.507504279879086,12.28628613516565,1.0400373750480867,35.047204108683921,-21.517287000552081,-2.1645070752729794,43.809005135854903,-5.5000865386853746E-2,-2.7835576833581399E-3,38.941337898537689,-4.4999134611662495E-2,-3.0365109792853673E-3,48.676672373172117,16.941287000553519,1.4360164512233098]
["A",0,27.499999999999936,0,27.499999999999936,34.374999999999922,12.010286135165495,{"$f":"4*E87-5*E91","v":0.95721077451761971},32.999999999999922,-7.5422870005525713,{"$f":"5*$E88-6*$E91","v":-0.71727473575521117},41.249999999999901,-4.7980008653864852,-0.22832676067008606,36.666666666666579,4.7550008653879354,0.30254087092357906,45.833333333333229,12.010287000553166,0.95721084372789278]

{"sheet":"Constants","index":5,"n_rows":25,"n_cols":7,"rows_kept":25,"cut":false,"hidden":true,"merged":[]}
["Constants"]
[]
[]
[]
[]
[]
[null,null,"1",100,"multiplier:",{"$f":"2^(1/12)","v":1.0594630943592953},"<--call this the \"semitone\""]
[null,null,"1#",{"$f":"D7*semitone","v":105.94630943592954},null,"by formula =2^(1/12)"]
[null,null,"2",112.24620483093732]
[null,null,"2#",118.92071150027213]
[null,null,"3",125.99210498948734]
[null,null,"4",133.48398541700348]
[null,null,"4#",141.42135623730957]
[null,null,"5",149.83070768766822]
[]
[]
[null,null,"continuing the series above…"]
[null,null,"5#",{"$f":"D14*semitone","v":158.74010519682002}]
[null,null,"6",{"$f":"D18*semitone","v":168.17928305074301},"octave:",{"$f":"D22/100","v":2.0000000000000013},"<--call this the \"octave\""]
[null,null,"6#",{"$f":"D19*semitone","v":178.17974362806797},"So the cent multiplier is =octave^(1/1200)"]
[null,null,"7",{"$f":"D20*semitone","v":188.77486253633882},null,{"$f":"octave^(1/1200)","v":1.0005777895065548},"<--call this the \"cent\""]
[null,null,"8",{"$f":"D21*semitone","v":200.00000000000014}]
[null,null,null,null,"Test the cent:"]
[null,null,null,null,"From the 5 to the 5# is 100 cents, or =150.00*(cent^100)"]
[null,null,null,null,null,{"$f":"D14*(cent^100)","v":158.74010519682054},"<--check!"]