The Tetrachord (Ancient). is one of the earliest known scales; it is ancient. It
was known in Babylon and Sumeria. This is a scale for the Kithara (Lyre), rather
than a Harp. The Harp was only a minor instrument in Sumeria and shunned by
the mainland Greeks. Tetrachord means four notes in Greek (cord can mean
either a string or note in Greek, in this case it is note because the various
tetrachord scales can be played quite well on a three string Greek Lyre). The
first note of the tetrachord is called the keynote or tonic, and the fourth string is
tuned to a perfect forth above the tonic. Any two equal strings whose length are
in the ratio of 4:3 will produce a perfect fourth (also 498.05 cents). The intervals
of the two notes between the first note and the fourth note are movable and are
moved to allow the stringed instrument to play the various Greek Modes. There
are three tetrachord modes: 1) the Enharmonic, 2) the Chromatic and 3) the
Diatonic (ancient Greek definitions of these words are different from modern
usage). The Enharmonic Mode is formed by two tones and two diesis. The
Chromatic Mode consists of two semitones and a tone and a half. The Diatonic
Mode is formed by two consecutive tones and a semitone. The movable notes
will have to fit in this interval of 498 cents by the following rules:
Quoting Sachs The Rise of Music in the Ancient World, East and West some Greek Modes and Shades:
“according to Aristonuxes:
interval from tonic
from second note to third third to fourth(fixed)
Enharmonic
398
49
49
Chroma malakon
Chroma hemiolion
Chroma toninion
364
348
298
66
74
99
66
74
99
Diatonon malakon
Diatonon syntonon
249
199
149
199
99
99
however Ptolemy disagreed, he chose:
Enharmonic
386
74
38
Chroma malakon
Chroma syntonon
316
267
120
151
62
80
Diatonon malikon
Diatonon toninon
Diatonon syntonon
Diatonon ditoniaion
Diatonon homalon
233
204
182
204
182
182
233
204
204
165
83
62
198
90
151”
Tetrachords can be extended to make larger scales with more range.
Consecutive tetrachords can be arranged two ways 1) the conjunct is where two
Teteachords are connected and share one string (for a total of seven strings) or
2) the disjunct where the two Tetrachords are separate and there is a tone ( 9:8
string length ratio) separation between the two Tetrachords (for a total of eight
strings). Again remember that the Tonic and the Forth are the fixed strings or
notes. The two strings between the tonic and forth are movable pitches;
however, the sum of their step size stays equal to a tone (9:8 step size) plus a
semi-tone (16:15 step size).
The scale The following on the scale is from the Ten Books of
Architecture by Vitruvius. The version available to us today is a summery of a
summary of a translation of a translation of a copy of a copy (after all the average
life of a copy is about a hundred years, so there had to be many copies and
some copyist had to make “improvements”). Vitruvius translated Aristonuxes
Greek into Latin and summarized. Vitruvius was copied and copied, with each
copier changing it a little. Then Dr. Morris Morgan translated the copy from
Valentine Rose’s Latin into English and cut the section on Aristonuxes short
saying what Vitruvius Summery just contained an obvious interpolation.
Valentine Rose’s copy added a grand staff to the section on Aristonuxes to help
explain the  Refer to Figure 2, the scale of Aristonuxe as quoted
from Vitruvius, Book V, Chapter IV, page XX. These scales are also called the
hexatonic and the octatonic scales.
The  of Aristonuxes of Tarentum (330 BC) is an 18-note scale that
spans two octaves. This two-octave span is supposed to be the range of male
voice. Rose, in his version of Vitruvius, stated that the lowest note is the A an
octave plus two notes below middle C and the highest note was the A above
middle C, but he gave no explanation of why he choose it to be this way. The
 is comprised of five Tetrachords and a few additional notes. Now refer
to Figure 2, and I will try to walk through how to form this scale (This scale almost
appears to be two scales push together so that the beginning and end are on the
same scale note, A. This results in a slight jumble of notes about in the middle of
the scale). The  scale is comprised of 8 fixed notes and 10 movable
notes. A technique that would be consistence with the technology at this time
would be to use a Monochord. I have built one for this purpose.
Now we will start with the fixed pitch strings and build the Harp scale. Take the
pitch of the tonic from some authoritarian source. Tune the pitch of the
Monochord to unison with this source. Now tune the pitch of the
Proslambanomenus string to unison with the Monochord. Note the Monochord
string’s vibrating length. Reduce this vibrating length by 8/9 and use this new
pitch to tune the Hypaton Hypate Harp String to unison. Note this vibrating
length on the Monochord and reduce it by 3:4 to get the pitch for the Meson
Hypate. Now tune the Meson Hypate Harp String to unison with the Monochord.
If at any time the Monochord runs out of range for the string it is currently using,
a string change will be required. With a string change, when one is going up the
scale, just remove the current string and insert the next lighter string, then go
back to one of the previously tuned strings on the Harp and pick up the correct
pitch and continue. The Synhemmenon Mese string will be 3:4 the vibrating
length of the string tuned to the Meson Hypate, so reduce the vibrating length of
the string in the Monochord and then tune the Synhemmenon Mese string to
unison with the Monochord. Again note the vibrating length on the Monochord
and reduce it by 3:4 to get the pitch step size to get to the Synhemmenon Nete.
Now tune the Synhemmenon Nete Harp string to unison with the Monochord.
Now it appears that a change in technique is required. Retune the Monochord
back to unison with the Synhemmenon Mese. Note the vibrating length on the
Monochord for the Synhemmenon Mese and then reduce this vibrating length to
1:2 to get the octave pitch. Now tune the Hyperbolaeon Nete Harp (highest)
String to unison with the Monochord. Now note the current Monochord vibrating
string length and increase the length by 4:3 to go down a perfect forth to the
Diezbugmenon Nete. Tune the Diezbugmenon Nete Harp String to unison with
the Monochord. Again, note the vibrating length of the Monochord string length
and increase its length further by 4:3 to go down to the Diezbugmenon
Paramese. Tune the Diezbugmenon Paramese Harp string to unison with the
Monochord. This concludes tuning the fix pitch strings, but as noted before this
gives a break in the middle of the scale between the Synmemmenon Tetrachord
and the Diezbugmenon Hexichord.
Figure 2 The  of Aristonuxes
The Synhemmenon Nete (highest note of the lower Tetrachord) is a pitch step
and a half above the Diezbugmenon Paramese (the lowest note of the higher
Tetrachord).
Confusion. To Quote Sachs, from The Rise of Music in the Ancient World, East
and West, pg222: “With all the Greek modes: Aeolian, Boeotian, Dorian, Iastian,
Ionian, Locrain, Lydian, Phryaian, with or without epithets; aneimene, chalara,
hyper, hypo, mixo, syntono, in an ever changing and often contradictory
terminology, impelled the methodical Greek philosophers to organize this chaotic
multiplicity of modes into one consistent system and eliminate those modes that
were not acceptable. As early as 400 BC the kithara had progressed to eleven
strings. Which in some pentatonic sequence covered exactly two octaves and
within had the possibility of representing the new system in its totality.”
The Greater Perfect Scale. The first section I extracted from Peter Fraser’s web
site and added the step sizes. I then followed this with a quotation from Sachs,
who had a better copy of Euclid to work from. Both are interesting.
Figure 3. The Greater Perfect Scale.
The Greater Perfect Scale (300 BC). Quoting Sachs, from The Rise of Music in
the Ancient World, East and West, pg222-223: “The Greek Philosopher and
Mathematician, Euclid first described the Perfect System or Systema teleion.
The Perfect Scale is a 15 note scale that covers just two octaves. However the
perfect system was more than just a double octave; it was perfect as a unique
attempt to organize the musical space from one center, (the note) a. The center
stands in its original octave of Dorian structure, e’-e, which, by adding half an
octave above and half an octave below, is extended to two octaves a’-A. This
new unit could shift both up and down by half an octave either way and thus
cover three octaves.
The notes added above and below the inner octave were named after the three
extreme notes at either end of it: nete, paranete, trite, above; lichanos,
parhypate, hypate below. Only the lowest note was given a name of its own;
the added note, proslambanomenos. The organization of the two octaves was
rather strange. Subdivision were neither octaves nor pentachords, but
tetrachords throughout. This implied two conjuncts at either end of the inner
octave and disjunction or diazeuxis in the middle. Reading downward, the
arrangement results in the tetrachord hyperbolaion, ‘of the exceeding notes’,
conjunct with the tetrachord diezeugmenon, which as the name said, was
disjunct from the tetrachord meson, ‘of the middle’ notes; this in was conjunct
with the tetrachord hypaton, ‘of the low’ (literally ‘high’) notes. The
proslambanomenos, ‘the left over’ note.
Naming of the notes of the Greater Perfect Scale
The somewhat cryptic remark “literally high” refers to a strange inversion in
Greek terminology: nete, the highest note (in our current terminology) means low
in Greek (or neat, short or small). Likewise, hypate, the lowest note means high
(or long or tall) in Greek.
Similarly the Greeks constructed a lesser perfect scale or systema teleion elatton
on the basis of the old heptad of two conjunct tetrachord. It is comprised of only
an eleventh, from d’ to A. The top tetrachord did not exist, and the disjunct
tetrachord diezugmenon was replaced by a conjunct tetrachord synemmenon:
Naming of notes of the Lesser Perfect Scale
I am not satisfied with Sachs use of letter to indicate the notes in his
representation of the Greater and Lesser Perfect Scale. Also these letters give
the wrong impression as to the intervals between the notes. The Perfect Scale is
a diatonic scale, the intervals between notes are: (Diatonic=unequal step sizes)
Tone Tone Tone Semitone Tone Tone Semitone, then next octave or Tone Tone
Semitone Tone Tone Tone Semitone. However, the Greeks did not use
instrumental music and only need an octave and a few notes to achieve all the
range that they wanted. The purpose of Greek music was to back a male singer
(they did not use female singers).
Quoting Sachs The Rise of Music in the Ancient World, East and West, pg225:
“Ptolemy, who lived in the second century AD, admitted seven keys, the centers
of which ascended diatonically from e to d’. With an attempt to keep “a” as the
common center.
There is a higher group of hyper scales, a lower group of hypo scales, and a
middle group without epithets. At first sight, all of them are similar Dorian keys;
but the modal structures are fundamentally different in the three groups:
The middle scales, based on disjunct tetrachords, have the fifth on the
top and are plagal.
2) The hyper scales based on conjunct tetrachords, with an additional
note above are likewise plagal.
3) The hypo scales based on conjunct tetrachords, with an additional note
below, have the fourth on top, or rather, should have the fourth on top
and be authentic. “
1)
Quote from Sachs The Rise of Music in the Ancient World, East and West,
pg234: “Aristides Quintilianus expressly states that voices did not span more
than two octaves. For this reason he adds that Dorian was the only key sung in
its total range. … Lyre players had similar limitations. … The consequences are
that music space, vague and shapeless in our music, became a palpable reality
in Greece. Each key had its own center, to be sure; but also music space as a
whole had its immovable center which, being the pitch tone was never neglected.
As a result, every melody had two foci; every note or group of notes gravitated
toward two different centers at once, toward the center of the individual key and
toward the center of the immovable perfect system. The first bearing was called
dynamis or mobile force, and the second, thesis or stationary force. A note
changed its dynamis according to its key; its thesis was immovable. The note e’
for example, was in all melodies nete kata thesin or highest stationary note,
whatever the key; but in Mixolydian, it was also mese katra dynamin or mobile
center, and in Lydian trite kata dynamin or mobile third from above. The mobile
and stationary functions coincided only in Dorian.
Look at a Greek melody from the dynamic center - b in Phrygian or d’ in
Mixolydian - finds the modal structure that we call Dorian; descending, the
sequence is to step through two whole tones and a concluding semitone to the
(dynamic) hypate. Things look different from the stationary center. The player,
adjusting his (Lyre to an) a and tuning the outer strings to e’ and e (the usual
range of melodies), realized that each transposition of the (Dorian) scale altered
the structure of his octave, since it shifted the semitone to places where
previously whole tones had been. The central rectangle in the above diagram
encases the resulting structure of all eight keys.
The Phrygian key, by one tone higher than the Dorian, sharped by two notes of
the central octave, c’ and f; thus the two central tetrachords become e’ d’ c#’ and
a g f# e: the semitone moved to the middle of the tetrachord and the original
Dorian octave changed to the Phrygian species. In the same way, the Lydian
key sharped d’ c’ g f and shifted the semitones to the upper ends of the
tetrachord that formed the central octave. Dorian as a key (Dorios tonos) created
a Dorian mode (Doristi harmonia) in the perfect system; a Dorian mode in the
perfect system could only originate if the melody followed the Dorian key. And
the same is true for Phrygian, Lydian, and the rest. Key and mode conditioned
each other and rightly were given the same tribal names.”
Now quoting from Jargenson, page 24: “Tuning to Fifths and Fourths are the
easiest intervals outside of the octave to tune because they exist next in order
after the octave in the Harmonic series. The ease of tuning Fifths and Fourths
along with their greater utility determined that Fifths and Fourths were to be used
for creating most of the practical scales from the beginning of history to the
present.
When the practice of tuning the pentatonic scale by means of a circle of fourths
and fifths became established, the following changes took place:
1) The fourths and fifths were made in tune enough to be used in vertical
sonorities.
2) Two of the wholetones (intervals between) became enlarged to
become a new interval named a minor third.
3) One of the fourths (intervals) became narrow enough to become a new
interval named a major third.
4) The new intervals listed above and their inversions resulted in minor
thirds, major thirds, minor sixths, and major sixths all being added to
the basic harmonic vocabulary of fourths and fifths; however, there
were still no semitones, tritones or major sevenths to make singing
difficult.
5) Strong tonality was developed in melodic compositions because the
scales were made permanently uneven.
6) One major triad along with its lower relative minor triad was
discovered.
Evidentially the phenomenon of Just Intervals was discovered and used for
tuning the fourths and fifths for two reasons: first, it is much easier to tune an
interval without beats than it is to temper an interval and guess how many beats
it should contain; second, the fifths and thirds can not be completely Just at the
same time, but fourths and fifths were chosen to be pure because the vertical
sonorities of the thirds and sixths were not yet important in harmony. The Just
fifth tuning practice must have been centuries old when Pythagoras began his
investigation into music. All the major and minor sixths and also the major and
minor thirds are each altered by one Syntonic comma from Just because all the
fifths are Just. The latter sixths and thirds are known as Pythagorean sixths and
thirds. Since these intervals are altered by the extreme of one Syntonic comma
each, their beat speeds are too fast to be objectionable because they seem to
disappear into a single tone. Pythagorean sixths and thirds have a tone color or
sound uniquely their own. “
Basic Pentatonic Scale (Ancient) (quoting from Jorgenson, now page 25)”In
this tuning there are two triads: namely the F Major and D Minor. There are two
major sixths and one minor third which are wide by one Syntonic comma. There
are two minor thirds which are narrow by a Syntonic comma. These intervals
which are altered by one Syntonic comma are known as Pythagorean intervals.
… This gives Pythagorean triads a certain rhythmic harmoniousness. …
This descending scale has intervals between notes in the ratio: F 27:32 D 8:9
C 27:32 A 8 :9 G 8:9 F. The cent values in round numbers are 294-204-294204-204. The Basic Pentatonic scale contains pure major tones of the 8:9 ratio,
pure fourths of the 3:4 ratio, pure fifths of the 2:3 ratio, minor sevenths of the 9:16
ratio and pure octave of the 1:2 ratio. There are no semitones, tritones or major
sevenths. All the triads and sixths are altered by the ratio 80:81 Syntonic
comma. The minor third ratio is 27:32; the major third ratio is 64:81; the minor
sixth ratio is 81:128 and the major sixth ratio is 16:27.
The line of fifths in the Pentatonic Scale is F C G D A. The bearing octave is F
below middle C to F above middle C. All fifths and fourths are pure. Major sixths
and minor triads are wide, minor thirds are narrow. Tuning steps:
1.
2.
3.
4.
5.
6.
7.
Tune middle C to tuning folk.
Tune F below middle C and F above middle C both pure to middle C.
Tune G below middle C pure to middle C.
Tune D above middle C to G below middle C pure.
Test the intervals for the purpose of finding possible mistake which should be corrected. In the
figure the numbers above the intervals indicate the beat speeds in beats per second in round
numbers.
Tune A below middle C pure to D above middle C.
Test all intervals.
”
Basic Pentatonic
(descending)
(step size)
Celtic Pentatonic
F
G
A
C
D
F
1/1 27/32
4/3 101/64 16/9
2/1
0
294
498 792
996
1200 cent value from tonic.
27/32 8/9
27/32
8/9
8/9
1/1
0
9/8
4/3
3/2
203.9 498.0 701.9
16/9
996.0
2/1
1200 cent value of tones from tonic.
It has been stated that the Celts organized their music in a pentatonic scale.
Since the Celts preferred to develop their memory and refrained from writing
anything down, one has to rely on their enemies for any historical record of their
customs.
It is highly likely that the gap scale Irish Harp music examples that are reported
by Bunting and other collectors are prehistoric Pentatonic Scales transposed to
historic Diatonic Scale or else works where the composer tried to make his music
sound this way.
Enharmonic Scale of Archytas (380 BC) Still quoting Jorgenson, page 31:
“This is a descending scale with the interval ratio of E 4:5 D 35:36 C 27:28 B
8:9 A 4:5 G 35:36 F 27:28 E. The cent value in round numbers for the
interval between pitches is 386 - 49 - 63 - 204 - 386 - 49 - 63.”
Eratosthenes Diatonic (230 BC) is also the Diatonic Ditoniaion published by
Claudius Ptolemy in 140 AD. Quoting Jorgenson, page 31:
“This scale is the basis of Western Music. In this tuning, the three basic primary
triads are developed. These are the G Major, C Major and F Major triads. Also,
the three lower relative minor triads E Minor, A Minor and D Minor are developed.
The formation of these triads creates the basic C Major tonality.
This descending scale has intervals between notes as: E 8:9, D 8:9, C 243:256,
B 8:9, A 8:9, G 8:9, F 243:256, E. The cent value in round numbers for the
step size between pitches are 204-204-90-204-204-204-90. The above scale
contains 243:256 ratio semitones, 512:729 ratio tritones and 128:243 major
sevenths in addition to all the intervals contained in the Basic Pentatonic Scale.
NOTE in Jorgenson’s method, pure means that an upper partial of one
pitch is in unison with an upper partial of the other note. Even though
Jorgenson did not like electronic tuners, the electronic tuner method of
tuning is faster than and as far as I can see better. In the electronic tuner
method, just tune to the closest 12 Tone Equal Temperament note, then
tune to the correct offset in cent. In the music below, the number above a
pair of notes is the beat frequency of a pair of their upper partials.
Tuning the Eratosthenes Diatonic Scale: In the Eratosthenes diatonic scale there
are six major and minor triads to the octave and all of them contain proportional
beat speeds. All the triads are Pythagorean triads. The line of fifths are F C G D
A E B. The bearing octave is E below middle C. All fifths and fourths are pure.
Major sixths and minor thirds are narrow.
Tuning Steps:
1.
2.
3.
4.
5.
Tune middle C to the Tuning Fork (unison zero beat).
Tune F below middle C pure to middle C (a fifth, a pair of upper partials have a zero beat).
Tune G below middle C pure to middle C (a fourth, a pair of upper partials have a zero beat).
Tune D above middle C pure to G below middle C.
Test
6.
7.
Tune A below middle C pure to D above middle C.
Test
8.
Tune E above middle C and E below middle C both pure to A below middle C. This creates the
interval EF which is the first semitone. The inversion FE is the first major seventh.
9.
Test
1.
Tune B below middle C pure to E above middle C and also check to see that it is pure to the E below
middle C. This creates the interval FB which is the first tritone.
11. Test
The Eratosthenes Diatonic Scale contains the following “Pythagorean” Triads:
The Pythagorean Triads are proportional as follows:
minor root = 0:1:1
minor first inversion = 1:1:0
minor second inversion = 1:0:1
major root position = 0:3:2
major first inversion = 3:4:0
major second inversion = 4:0:3”
Chromatic Scale of Didymium (30 BC) Still quoting Jorgensen, page 31: “This
is a descending scale with the interval ratio E 5:6 D 24:25 C 15:16 B 8:9 A
5:6 G 24:25 F 15:16 E. The cent value in round numbers for the interval
between pitches is 316 - 70 - 112 - 204 - 316 - 70 - 112. Pure minor tones, minor
thirds, major thirds, minor sixths and major sixths. There are pure ratio 24:25
semitones so small that they could be classified as large third tones.
Diatonic Syntonon of Ptolemy (140 AD) Also known as the Diatonic Scale of
Didymium (30BC). Still quoting Jorgenson, page 31: “This is a descending
scale with the interval ratio of E 9:10 D 8:9 C 15:16 B 8:9 A 9:10 G 8:9 F
15:16 E. The cent value in round numbers for the interval between pitches is
182 - 204 - 112 - 204 - 182 - 204 - 112.
In this scale all the ratio 64:81 Pythagorean major thirds and Pythagorean minor
sixths were changed into pure 4:5 major thirds and pure 5:8 minor sixths. Three
of the minor thirds and three of the major sixths were also made pure. The
interval of a fourth between A D was altered by one Syntonic comma to have a
new ratio of 20:27 which is an out of tune wolf interval. The fourth A D was
ruined out of necessary in order to gain all pure thirds and sixths. There are both
major and minor whole tones in this scale. The three primary triads: G, C, and
F are in Just intonation. Ptolemy’s Diatonic Syntonon is the ancestor of the
Common Model Just Tuning as outlines in Marpug’s Monochord No.1. The
Ptolemy diatonic scale is more harmonious than the Eratosthenes diatonic scale,
but lacks the utility of the Eratosthenes. This conflict between harmoniousness
and utility lead to the difference between the Meantone temperament and the
Well temperament.”
Diatonic Hemiolon of Claudius Ptolemy (140 AD) Still quoting Jorgenson,
page 31: “This is a descending scale with the interval ratios of E 9:10 D 10:11
C 11:12 B 8:9 A 9:10 G 10:11 F 11:12 E. The cent value in round numbers
for the interval between pitches is 182 - 165 - 151 - 204 - 182 - 165 - 151.”
Music Theory of Anicius Manlius Boethius (520 AD) Boethius read a
reference that stated that Pythagoras had perfected a diatonic scale based on
fifths (not possibly true) and Boethius tried to find this scale. Boethius found
Eratosthenes Diatonic scale instead and incorrectly named it the Pythagorean
Diatonic; so from this time on, to avoid additional confusion Eratosthenes scale is
now called the Medieval Pythagorean Diatonic scale. Boethius also got caught in
the confusion of whether Greek scales ascend or descend and he got it wrong.
Next he got the names of the Greek Modes incorrect. But Borthius was not the
only Medieval Music Theorist that got the Greek Modes names incorrect. The
modes known as the Church Modes are the results of this mistake.
Medieval Pythagorean Scale (of Boethius) This scale is called in error the
Medieval Pythagorean Diatonic Scale. This is wrong for two reasons: one,
Boethius misnamed the Diatonic Scale of Eratosthenes and two this scale is
more than a diatonic scale it has four chromatic notes added: Bb, Eb, F# and
C#. But it is a very useful scale and is a good scale in which to compose.
Quoting Jorgenson, page 45: “This is the Eratosthenes diatonic scale with four
chromatic tones added. There are still no wolf interval. In this tuning there are
eighteen major and minor triads to the octave, and all of them contain
proportional beat speeds. The C# minor, C# major, E major, F minor G# minor
and Ab major triads still do not exist in this scale. The line of Just fifths is: Eb,
Bb, F, C, G, D, A, E, B, F#, C#.
In this scale, there is a new kind of interval created which is known as a schisma
interval. These intervals are each altered from Just intonation by the extremely
small amount of one schisma, which in round numbers is only 2 cent in size.
With Schisma intervals it is almost impossible to tell that they are different from
Just interval. They are altered intervals, but they are never directly tempered by
ear. Schisma intervals exist because they are the end result of lines or groups of
other pure intervals. The diminished fourths: C# to F, F# to Bb and B to Eb all
sound quasi pure because they are actually narrow major thirds. The augmented
seconds: Bb to C#, and Eb to F# both sound quasi pure because they are
actually wide schisma minor thirds.”
Tuning Steps for Medieval Chromatic Pythagorean Scale: (quote from
Jorgenson, page 48)
Use the eleven steps for tuning the Eratosthenes scale (from this paper, page
25) then
12. Tune Bb below middle C pure to F below middle C.
13. Test
14. Tune Eb above middle C pure to Bb below middle C.
15. Test
16. Tune F# below middle C pure to B below middle C.
17. Test
18. Tune C# above middle C pure to F# below middle C.
19. Test
Medieval Modes and Music Theory of Guido of Arezzo (1050 AD)
Developed four line staff and the Ut Re Mi Scale. Established the Church Modes
as Dorian, Phrygian, Lydian, Mixolydian and maybe the Locrian (some authorities
deny that the Locrian is a mode). No matter, the scales of Guido were different
from the correct Greek modes. The correct knowledge was still readily available
in Constantine (Eastern Roman Empire, official language was Greek), so it is a
wonder that no one bothered to go obtain it? Christian Monks and people in
trade were making the trip.