Troparion by Cassia, Triplex, instrumental
Fine tuning by GKM 2016
(Petros and Iakovos of Peloponnesos, and Chourmouzios)
(
http://www.mediafire.com/download/9..._Melodos_2016_Cassia_Triplex_RVRB_ison_LQ.zip) 68MB
Τροπάριον Κασσίας μοναχῆς
μάθημα Γεωργίου Χουρμουζίου Χαρτοφύλακος
ἀντίστοιχον τοῦ
"καλοσυγκερασμένου κλειδοκυμβάλου"
(
http://analogion.com/forum/showpost.php?p=202555&postcount=69)
(
http://analogion.com/forum/showpost.php?p=202468&postcount=68)
ΓΚΜ Τροπάριον Κασσιανῆς ἀργόν, Νικολάου Πρωτοψάλτου
(
http://analogion.com/forum/showpost.php?p=202019&postcount=65)
Fine tuning of psaltiki using Melodos, Melodyne and Sonic Visualizer
has led to the conclusion that just intervals, including fifths and octave, sound "flat".
Tuning using 68ET and Golden section intervals of a just octave scale leads to better approximations (larger tone and fifths).
The last daring experiment was to augment the octave to 2010cents.
The overalls intervals are presented below and are compiled in the melodos file (from which they may be extracted).
Octachord: diatonic = 2010 cents
Tetrachords: Diatonic = Enharmonic = 490 cents
Pentachords: Diatonic = Chromatic 711 cents
Pentachord: Enharmonic (720c) > Golden Section 716 > Diatonic (711)
Chromatic does NOT have same octave as Diatonic (2010c) and Enharmonic
During fine tuning:
Some fifths of 711c were reduced to 709c
Some diphonos 355c intervals were maintiained, but the itermediate value altered
So hyphesis as "elxeis" does not seem to work in the melodos scales created, and all were added manually in the midi file.
Intervals were adjusted according to the ONE ison theory, that is, ANY fthora change, even parachordal, MUST compatible with a non varying ison... this requires "elasticity" of intervals and, according to this experiment, only chromatic intervals required minute changes.
A challenge is put forth to those insisting on Epitropi and Karas theories to use the files, to adjust intervals according to those theories, and to make them public.
A few typographical errors exist in melodos (the score was obtained from Melodos' OCR"
Golden Section
excel equation
=(AH73/(4*((1+((5)^(1/2)))/2)-1))
=(AH73/((4*((1+((5)^(1/2)))/2)-1))*(((1+((5)^(1/2)))/2)-1))
=((B3-((3*C3)+(2*D3))*(1/2)))
Diphonic trichord Golden Section
219.7c
135.8c
Diatonic tetrachord
212.0
161.4
125.6
The latter two may be slightly augmented (+ 5 cents) in some cases
=======
Enharmonic tetrachord 01
230
48
212
Enharmonic tetrachord 02
212
66
212
66
212
Kliton
66
212
Di ga 48
ga bou 162.0
bou pa 212
pa Ni 288
or
Kliton
66
212
Di ga 48
ga bou 212
bou pa 212
pa Ni 238
Spathi
BouPa 230.0
PaNi 130.0
Ni Zo 230
Zo Ke 130.0
Ke Di 130.0
Di Ga 230
Ga Bou130.0
Bou Pa230
Pa Ni 212
Spathi
BouPa 230
PaNi 130.0
Ni Zo 230
Zo Ke 130.0
Ke Di 230
Di Ga 130.0
Ga Bou130.0
Bou Pa230
Pa Ni 212
Zygos
Ke Di 212
Di Ga 130.0
Ga Bou 230
Bou Pa130.0
Pa Ni 230
Other
230.0 125.5
(230+68) (125.6 - 68)
294 61.5
(711-212)=499
========
Κύριε, ἡ ἐν πολλαῖς ἁμαρτίαις περιπεσοῦσα Γυνή, τὴν σὴν αἰσθομένη Θεότητα, μυροφόρου ἀναλαβοῦσα τάξιν, ὀδυρομένη μύρα σοι, πρὸ τοῦ ἐνταφιασμοῦ κομίζει. Οἴμοι! λέγουσα, ὅτι νύξ μοι, ὑπάρχει, οἶστρος ἀκολασίας, ζοφώδης τε καὶ ἀσέληνος, ἔρως τῆς ἁμαρτίας. Δέξαι μου τὰς πηγὰς τῶν δακρύων, ὁ νεφέλαις διεξάγων τῆς θαλάσσης τὸ ὕδωρ· κάμφθητί μοι πρὸς τοὺς στεναγμοὺς τῆς καρδίας, ὁ κλίνας τοὺς οὐρανούς, τῇ ἀφάτῳ σου κενώσει· καταφιλήσω τοὺς ἀχράντους σου πόδας, ἀποσμήξω τούτους δὲ πάλιν, τοῖς τῆς κεφαλῆς μου βοστρύχοις, ὧν ἐν τῷ Παραδείσῳ Εὔα τὸ δειλινόν, κρότον τοῖς ὠσὶν ἠχηθεῖσα, τῷ φόβῳ ἐκρύβη. Ἁμαρτιῶν μου τὰ πλήθη καὶ κριμάτων σου ἀβύσσους, τίς ἐξιχνιάσει ψυχοσῶστα Σωτήρ μου; Μή με τὴν σὴν δούλην παρίδῃς, ὁ ἀμέτρητον ἔχων τὸ ἔλεος.
Κύριε, ἡ ἐν πολλαῖς ἁμαρτίαις περιπεσοῦσα Γυνή, τὴν σὴν αἰσθομένη Θεότητα, μυροφόρου ἀναλαβοῦσα τάξιν, ὀδυρομένη μύρα σοι, πρὸ τοῦ ἐνταφιασμοῦ κομίζει. Οἴμοι! λέγουσα, ὅτι νύξ μοι, ὑπάρχει, οἶστρος ἀκολασίας, ζοφώδης τε καὶ ἀσέληνος, ἔρως τῆς ἁμαρτίας. Δέξαι μου τὰς πηγὰς τῶν δακρύων, ὁ νεφέλαις διεξάγων τῆς θαλάσσης τὸ ὕδωρ· κάμφθητί μοι πρὸς τοὺς στεναγμοὺς τῆς καρδίας, ὁ κλίνας τοὺς οὐρανούς, τῇ ἀφάτῳ σου κενώσει· καταφιλήσω τοὺς ἀχράντους σου πόδας, ἀποσμήξω τούτους δὲ πάλιν, τοῖς τῆς κεφαλῆς μου βοστρύχοις, ὧν ἐν τῷ Παραδείσῳ Εὔα τὸ δειλινόν, κρότον τοῖς ὠσὶν ἠχηθεῖσα, τῷ φόβῳ ἐκρύβη. Ἁμαρτιῶν μου τὰ πλήθη καὶ κριμάτων σου ἀβύσσους, τίς ἐξιχνιάσει ψυχοσῶστα Σωτήρ μου; Μή με τὴν σὴν δούλην παρίδῃς, ὁ ἀμέτρητον ἔχων τὸ ἔλεος.
Κύ- -ρι- -ε, ἡ ἐν πολ- -λαῖς ἁ- -μαρ- -τί- -αις πε- -ρι- -πε- -σοῦ- -σα Γυ- -νή, τὴν σὴν αἰ- -σθο- -μέ- -νη Θε- -ό- -τη- -τα, μυ- -ρο- -φό- -ρου ἀ- -να- -λα- -βοῦ- -σα τά- -ξιν, ὀ- -δυ- -ρο- -μέ- -νη μύ- -ρα σοι, πρὸ τοῦ ἐν- -τα- -φι- -α- -σμοῦ κο- -μί- -ζει. Οἴ- -μοι! λέ- -γου- -σα, ὅ- -τι νύξ μοι, ὑ- -πάρ- -χει, οἶ- -στρος ἀ- -κο- -λα- -σί- -ας, ζο- -φώ- -δης τε καὶ ἀ- -σέ- -λη- -νος, ἔ- -ρως τῆς ἁ- -μαρ- -τίας. Δέ- -ξαι μου τὰς πη- -γὰς τῶν δα- -κρύ- -ων, ὁ νε- -φέ- -λαις δι- -ε- -ξά- -γων τῆς θα- -λάσ- -σης τὸ ὕ- -δωρ· κάμ- -φθη- -τί μοι πρὸς τοὺς στε- -ναγ- -μοὺς τῆς καρ- -δίας, ὁ κλί- -νας τοὺς οὐ- -ρα- -νούς, τῇ ἀ- -φά- -τῳ σου κε- -νώ- -σει· κα- -τα- -φι- -λή- -σω τοὺς ἀ- -χράν- -τους σου πό- -δας, ἀ- -πο- -σμή- -ξω τού- -τους δὲ πά- -λιν, τοῖς τῆς κε- -φα- -λῆς μου βο- -στρύ- -χοις, ὧν ἐν τῷ Πα- -ρα- -δεί- -σῳ Εὔ- -α τὸ δει- -λι- -νόν, κρό- -τον τοῖς ὠ- -σὶν ἠ- -χη- -θεῖ- -σα, τῷ φόβῳ ἐ- -κρύ- -βη. Ἁ- -μαρ- -τι- -ῶν μου τὰ πλή- -θη καὶ κρι- -μά- -των σου ἀ- -βύσ- -σους, τίς ἐ- -ξι- -χνι- -άσει ψυ- -χο- -σῶ- -στα Σω- -τήρ μου; Μή με τὴν σὴν δού- -λην πα- -ρί- -δῃς, ὁ ἀ- -μέ- -τρη- -τον ἔ- -χων τὸ ἔ- -λε- -ος.
Diatonic Octave 1210
Enharmonic tone 230
Enharmonic smallest 48
Diatonic Meizon ratio (12:9:7) 12
Diatonic Elasson ratio (12:9:7) 9
Diatonic Elachistos ratio (12:9:7) 7
Calculated diatonic Meizon 212.0
Pentachordon (E) 720.0
Pentachordon (D) 711.0
Pentachordon (C golden section) 715.6
Pentachordon (D=C) 711.0
Pentachordon (C 38/64ET) 718.4
Tetrachordon (D=E) 490.0
Trichordon (C Golden Section) 357.8
Trichordon (Common OctaPentaChord) 355.5
Trichordon (C (12+7)64ET) 359.2
Diatonic Elasson (12:9:7) 161.4
Diatonic Elachistos (12:9:7) 125.6
Diatonic Pentachordon Test 711.0
Diphonias Megas Golden Section (octave) 221.1
Diphonias mikros Golden Section (octave) 136.7
Diphonias Megas 12/64ET 226.9
Diphonias Micros 7/64ET 132.3
Diphonias Megas (Common OctaPentaChord) 212.0
Diphonias Micros (Common OctaPentaChord) 143.5
355.5
Diphonias Megas Golden Section (fifth) 219.711083
Diphonias mikros Golden Section (fifth) 135.8
Diphonias Penctachord Test 711
Spatheion Megas 230.0
Spatheion Mikros 125.5
