If remember tetrachord (t_c)
Vilen
Such construction of octave scale has advantage that first t_c
supports the second one thank to horizontal ties between their
overtones. The 3. overtone of each note in first tetrachord coincides
with the second overtone of corresponding note in the second.
The concept of tetrachord is very near but possibly more sapid than
concept of fifth interval which is basis of all music theories
(J.Rameau-major and minor chords, H.Riemann-dominant and subdominant,
H.Schenker-ursatz).
Ancient Greeks built the octave scale from 2 same t_c (with same
intervals) each of which has 4 notes embracing interval 4/3 so the
begin of second t_c is on interval fifth from scale's begin.
Below I try to use analysis of tetrachord constructions in different
modes together with devices of leading note and chords in order to
understand process of ousting church modes by major-minor modes and
properties of last ones.
The Dorian defgabcd and Lydian fgabcdef were most popular modes in
Medieval. The Dorian includes semitone intervals 212-2-212 and thus
has structure with 2 same t_c but hasn’t leading note to tonic of
scale. The Lydian includes semitone intervals 222-1-221 and thus
hasn’t structure with 2 same t_c but has leading note to tonic of
scale. It is important that tonic note wasn’t center of melody then.
With development of harmonic the most consonant triads were found:
major- ceg,fac,gbd and minor-ace,dfa,egb. These triads were used
together with church modes.
One of functions which chords(triads) can fulfill is providing of
horizontal ties. Such ties are better provided if used on time
intervals triads and their notes forms chains of the same type
triads. It is possible(in given diatonic scale) only one such chain of
major triads fac,ceg,geb and only one of minor ones-dfa,ace,egb. These
chains may be derived from correspondingly Lydian and Dorian modes.
Apparently the middle link are most significant in each of these
chains as it is tied with 2 other triads. Because of that from Lydian
scale is major scale cdefgabc obtained and from Dorian-minor scale
abcdefga.
Let us compare constructions of t_c in joining triads of these scales.
Joining tonic and dominant triads of major scale has structure(with
intermediate notes) 221-2-221 i.e. includes same t_c, In minor there
is structure 212-2-122 i.e. includes different t_c,
Analogous joining subdominant and tonic triads have structures: in
major- 222-1- 221 and in minor-
212-2-212.
Thus the major scale is better from the viewpoint of horizontal ties
of intermediate notes in case of using joining tonic and dominants
triads and minor scale - in case of joining subdominant an tonic
triads.
This consideration asserts that main properties of major and minor
triads are determined by their position in the scale and structure of
corresponding t_c and but not their reference to fundamental bass.
Confusion in this question is arises as music scale is built on basis
of overtone series which were the only possible means for building of
music scale. Even Aristoxenus who believed that music scale must be
build on natural for ear intervals of equal temperament was compelled
to use second and third overtones.
Yuri Vilenkin
J. B. Wood
<7d53a455-4817-4782...@k4g2000yqb.googlegroups.com>, Vilen
<vi...@online.de> wrote:
> Such construction of octave scale has advantage that first t_c
> supports the second one thank to horizontal ties between their
> overtones. The 3. overtone of each note in first tetrachord coincides
> with the second overtone of corresponding note in the second.
Hello, and are we talking about the use of octaves for music performance
by the ancients? The above is just another way of stating that the pitch
ratio of a just perfect fifth is 3/2. Assuming that polyphony had limited
or no application in ancient music composition and performance what is
this octave advantage you state? You also have to consider the impact of
numerologists of the time. Also, the starting point for deriving a lot of
the ancient tunings by Ptolemy, Didymus, Archytas and others was the
perfect fourth ratio of 4/3 rather than the fifth (which of course can be
derived from the 4th assuming a 2/1 octave).
Granted, in a diatonic scale consisting of two tetrachords, the upper
tetrachord becomes the lower tetrachord when modulating/changing key
upward by a fifth.
Half of a C major scale is carried along to a G major scale. But I'm not
sure modulation was an issue with the ancients, either.
> The concept of tetrachord is very near but possibly more sapid than
> concept of fifth interval which is basis of all music theories
> (J.Rameau-major and minor chords, H.Riemann-dominant and subdominant,
> H.Schenker-ursatz).
It would appear that the fifth is the basis for generating the historical
tunings (just, meantone family (including Pythagorean and ET) and
irregular temperament trade-offs) used in Western music. This doesn't
apply to all tuning systems used in all cultures, however. "Sapid"?
(typo?) Sincerely,
John Wood (Code 5550) e-mail: wo...@itd.nrl.navy.mil
Naval Research Laboratory
4555 Overlook Avenue, SW
Washington, DC 20375-5337
Vilen
>Hello, and are we talking about the use of octaves for music performance
>by the ancients? The above is just another way of stating that the pitch
>ratio of a just perfect fifth is 3/2. Assuming that polyphony had limited
>or no application in ancient music composition and performance what is
>this octave advantage you state? You also have to consider the impact of
>numerologists of the time. Also, the starting point for deriving a lot of
>the ancient tunings by Ptolemy, Didymus, Archytas and others was the
>perfect fourth ratio of 4/3 rather than the fifth (which of course can be
>derived from the 4th assuming a 2/1 octave).
I cite from the page
http://science.jrank.org/pages/9577/Harmony-Harmony-in-Ancient-Greek-Writings-on-Music.html:
“In ancient Greek writings on the subject of music, harmony (also
known as "harmonics") was the study of the formation of melody This
study began with the elements of melody—the individual notes—and
continued with the specification of appropriate ways in which pairs of
notes, a higher and a lower, could be combined successively into
melodic intervals. (The simultaneous combination of notes was not a
part of classical Greek musical practice.) These melodic intervals
were in turn combined into a variety of complex scalar systems, the
defining structures of complete melodies. In general terms, classical
Greek harmonics falls into two traditions: the Aristoxenian and the
Pythagorean.”
I think that ancient Greeks understood that perception of a note
depends from previous notes (especially last one) and tried to find
harmonic in this sense. Now it is clear that this dependence is
determined by common frequency components. Besides it is necessary to
take in consideration pure technical aspect: even without intention
different notes can sound partly in the same time and make undesired
dissonances. Of course, notions of key, chord, modulation are out of
question.
>It would appear that the fifth is the basis for generating the historical
>tunings (just, meantone family (including Pythagorean and ET) and
>irregular temperament trade-offs) used in Western music. This doesn't
>apply to all tuning systems used in all cultures, however.
Besides western music culture tone ratios 2 and 3 are used in
African, Arabian, Indian, Chinese, Japan and Java music ( last one
has even system of music notation). Other cultures are less
significant and because of absence of science haven't “ impact of
numerologists“
Sincerely,
Yuri Vilenkin
Vilen
>Now it is clear that this dependence is determined by
>common frequency components
Correction:
Now it is clear that this dependence is determined by
common and near frequency components.
Yuri Vilenkin
Jack Campin - bogus address
> African, Arabian, Indian, Chinese, Japan and Java music (last
> one has even system of music notation).
You are writing as if these intervals are universally regarded as
a desirable thing. They aren't.
Japanese music has the Noh flute, whose scale lacks an octave, and
Javanese music has the slendro scale which lacks the fifth. That
is, both cultures knew about the octave and fifth, but preferred to
do without them for certain kinds of music.
Ordinary church bells don't have fifths and octaves either (the
carillon is a relatively recent invention). For the purposes of
English bellringing, all that matters is that you have a range of
distinct pitches. And that idiom coexists in a culture that has
many other kinds of more precise tonality. People going to church
could start singing psalms in the mediaeval modal system before
the atonal reverberations of the bells had died away.
A more recent example: the sounds used for fruit machines often
use a scale in which the frequencies are in arithmetic progression
(it's easier to program simple microchips that way, and the sound
was fixed back in the 70s, so they've maintained the same tonal
system for the sake of familiarity). Most of the intervals you
get from that have nothing in common with any familiar musical
scale from anywhere, but they're certainly music to the ears of
a gambler.
Musical systems don't necessarily replace each other in evolution
any more than biological ones do. Coexistence is the norm.
==== j a c k at c a m p i n . m e . u k === <http://www.campin.me.uk> ====
Jack Campin, 11 Third St, Newtongrange EH22 4PU, Scotland == mob 07800 739 557
CD-ROMs and free stuff: Scottish music, food intolerance, and Mac logic fonts
****** I killfile Google posts - email me if you want to be whitelisted ******
Vilen
wrote:
>You are writing as if these intervals are universally regarded as
>a desirable thing. They aren't.
I said only that these intervals are used in those cultures,
possibly, with other ones. The matter isn't desire but manifestation
of physical laws.
>Musical systems don't necessarily replace
>each other in evolution
>any more than biological ones do.
>Coexistence is the norm.
I think that biological evolution isn’t best thing to compare.
What is musical system? By intuitive understanding it is determined
by laws of human sound perception and existing technique. For example
the appearance of major-minor systems were impossible without key
instruments. The sound perception is object of biological evolution
which is very slow even in scale of civilizations. Development of
technique leads to renovation of musical system. Naturally, in some
time intervals old and new systems must coexist, even several
generations of them.
Best Regards
Yuri Vilenkin
Orangeboxman
part of classical Greek musical practice.)
Oblique harmony nonetheless results when melodies are played on the
lyre (or similar instruments
such as ancient Greeks are believed to have considered for reference
in this matter), unless each string
is silence as or before the next string sounds.
It's my guess that they might have experimented at some
point with not doing that.
Maybe?