MUS 573 Cumulative

Survey of Music Theory

Is Andrew Barker (the author of Harmonics in Classical Greece) a musicologist or a classicist?

Classicist

What does barker claim is the "most obstructive difficulty" to studying Greek harmonics?

Few surviving early texts; Its history must be reconstructed from others authors' writings; Evidence we have on the subject cannot always be taken at face value.

Study of the patterns formed by lengths of syllables in verse, whether it is set to "music" or not

Metrics

Study of the patterns within which a singer or instrument's sequence of long and short syllables and/or notes are divided and grouped into repeated rhythmical structures; roughly analogous to the 'bars' of modern music

Rhythmics

The study of the structures underlying melody; identification and analysis of the varieties of scales and systems of attunements that could be reckoned as musical

Harmonics

Which is the most important of the three Greek musical sciences?

Harmonics

Which Greek author includes rhythmics as a substantial discipline?

Aristoxenus

Theoretical writers of the fourth century unanimously agree that there is an objective and discernible line of demarcation, independent of human whim, decision, or ingenuity, between musically well-ordered relations and transformations on the one hand, and on the other the indeterminate chaos of the non-musical. (True/False)

True

Barker suggests that harmonics had little or nothing to do with the realities of Greek musical practice. (True/False)

False. While this is a common assumption, Barker argues the opposite.

The Greater and Lesser Perfect systems comprise a regular scheme which formed the background to Aristoxenian analysis. (True/False)

True

Within the perfect systems, what gives each note its identity?

Its relations to other notes in the system

Two tetrachords are separated by one tone (major second)

disjunction

Group of four notes, of which the outermost are a perfect fourth apart

tetrachord

The highest note of the lower tetrachord is also the lowest note of the tetrachord above

conjunction

In the Greek perfect systems, the second word of a note name identifies what?

Its tetrachord

How many octaves are in the Greater Perfect System?

2

The "proslambanomenos" is the highest note in the Greater Perfect System (True/False)

False - it is the LOWEST note in the Greater Perfect System

In the Aristoxenian tradition, what are the names of the three genera created by shifting the notes inside of the tetrachords?

Enharmonic, Diatonic, Chromatic

What is the range of the Lesser Perfect System?

An octave plus a fourth

In the Greater Perfect System, the tetrachord above the meson is (conjunct/disjunct)?

Disjunct

In the Greater Perfect System, the tetrachord above the meson is called the?

diezeugmenon

In the Lesser Perfect System, the tetrachord above the meson is (conjunct/disjunct)?

conjunct

In the Lesser Perfect System, the tetrachord above the meson is called the?

synemmenon

Ancient Greek writers tended to use what term for "high"?

oxys (sharp)

Ancient Greek writers tended to use what term for "low"?

barys (heavy)

One difficulty with ancient Greek terminology is that 'sharp' and 'heavy' are not direct contraries, meaning they cannot be directly compared. (True/False)

True

The Greek word for 'pitch'

tasis

The meaning of the Greek word for 'pitch'

tension

According to Barker, harmonic analysis absolutely requires what?

A system of measurements to express pitch relationships quantitatively

Attempted to identify musical units by using the ear. Working toward a quasi-linear conception of pitch by thinking of the relationships between pitches as gaps.

Unidentified Music Theorists in Plato's Republic

Represented relationships between pitches as ratios of numbers. Measured audible 'concords.'

The Pythagoreans

Pythagorean Ratio for Perfect Fourth

4:3

Pythagorean Ratio for Octave

2:1

Pythagorean Ratio for Perfect Fifth

3:2

The monochord (or 'kanon' in Greek) is first recorded after when?

The late fourth century

When Archytas discusses how higher and lower notes are produced, what instrument does he mention?

auloi

Roman writers tell us that Pythagoras 'demonstrated the ratios of the concords' on various instruments, which all produced the expected results. (True/False)

False - several do not yield the required results

Archytas claims that high-pitched notes move more (quickly/slowly)

quickly

Archytas claims that low-pitched notes move more (quickly/slowly)

slowly

Pythagorean ratios give direct descriptions of our musical perceptions as we perceive it. (True/False)

False

Aristoxenus claims the Pythagorean approach to musical ratios is irrelevant to music and harmonic science because the ratios are not directly perceptible to our hearing. (True/False)

True

What author transferred Greek mathematical harmonic theory into Latin, bringing it into the Medieval tradition?

Boethius

Which of Boethius's writings does Barker cite as being "especially revered" in the Middle Ages?

'Consolations of Philosophy'

What three individuals did Ptolemy specifically name as writers on harmonics prior to himself?

Didymus, Archytas, and Aristoxenus

Somewhere in the middle: reason and perception are equally important, but with different roles. Properly reasoned conclusions cannot conflict with evidence of the senses, and a theorist must accept any conclusions reached by reason from a perceptual starting point.

Aristoxenians

Primarily used reason. Perception was only a 'spark' to kindle the fires of reason. If conclusions conflict with evidence of the senses, then the senses must be mistaken.

Pythagoreans

Focused on perception, minimal use of reason. These train musicians and judge students' efforts entirely by ear.

Instrumentalists/Voice-trainers

By the end of the fourth century, what were the two primary schools of thought most writers on harmonics aligned with?

Aristoxenian and Pythagorean/mathematical

Give the date for this author: Aristides Quintillianus

3rd century AD

Give the date for this author: Nichomachus

~100 AD

Give the date for this author: Gaudentius

3rd-4th century AD

Who wrote 'Introduction to Harmonics'?

Nicomachus

Who wrote 'Elementa harmonica'

Aristoxenus

Who wrote 'De Musica'

Aristides Quintillianus

Which four authors are especially useful to modern scholars because they faithfully preserve much of the work of Aristoxenus?

Cleonides, Bacchius, Gaudentius, and Aristides Quintillianus

The primary surviving Aristoxenian texts largely seem to have been written for what purpose?

as textbooks

Ptolemy's goal is to show that all systems that ________ recognizes as musically well-formed conform to _________ principals

the ear; mathematical

Although most of Ptolemy's 'Harmonics' deals with audible melodies, Book 3 also deals with corresponding patterns of relations in which two areas?

the heavens and the human soul

While his writings are similar to the contemporary Platonists, Nichomachus's work present themselves as explorations of ancient Aristoxenian traditions (True/False)

False - Nichomachus was a Pythagorean, and saw Plato as a record of Pythagorean thought.

According to Barker, whose work in its Boethian version did most to give medieval Europe its picture of Greek harmonic theory?

Nichomachus

Nichomacus and other writers who followed Plato primarily worked with which genera or scale?

diatonic

Nichomachus was not seriously concerned with the actual attunements of musical practice. (True/False)

True

Boethius represents the study of music through reason as superior to the arts of performers and composers. (True/False)

True

Two notes are physically consonant when the frequency ratio is a ratio of (low/high) integers.

Low

The difference in tuning between “F-sharp” and “G-flat” when each scale has been generated by the Pythagorean system is known as the _________________.

Pythagorean comma

R. Bonsanquet’s nineteenth-century harmonium divided an octave equally into how many notes?

53

What is the basic premise of Equal Temperament?

Each note is generated by a single basic interval

Just intonation uses the simple ratio of _____________ for the major third, while equal temperament’s ratio of ____________________ is noticeably (sharp/flat) to an ear that is used to the extreme consonance of the just major third.

1.25; 1.259921…; sharp

Which intervals are adjusted in Just Intonation relative to Pythagorean Tuning in order to be more consonant (have simpler frequency ratios)?

Thirds and Sixths

A scale tuned in Just Intonation after Zarlino has two different whole tones (major and minor), the difference between these two frequency ratios is 81/80 or 1.0125. This difference is called what?

syntonic comma

What problem arises when you attempt to transpose a Just Intonation scale up by a fifth?

The scale includes 2 new notes

One notable proponent of Just Intonation from venice was named _______________________. He published ______________________ in the year ____, which included a mathematical description of a Just Intonation scale.

Giuseppe Zarlino; Institutioni harmoniche; 1558

What is the size of a Pythagorean Comma?

3¹²/2¹⁹ or 1.01364

Simon Stevin’s suggestion to equally divide the octave into 12 semitones was quickly adopted and was the standard in Western music by his death in 1620. (True/False)

False - By the 1700s the idea of Equal Temperament was relatively new, and not widely practiced until later in that century.

One practical result of Just Intonation is that fixed-pitch instruments needed new pitches for each successive key. In 1636, Martin Mersenne described a keyboard with how many keys to play in Just Intonation?

31

The oldest system of scale construction is described as the ____________.

Pythagorean Scale

(Match the Pythagorean ratios to their intervals) 9/8

Whole Tone

(Match the Pythagorean ratios to their intervals) 2/1

Octave

(Match the Pythagorean ratios to their intervals) 243/128

Major Seventh

(Match the Pythagorean ratios to their intervals) 256/243

Semitone

(Match the Pythagorean ratios to their intervals) 27/16

Major Sixth

(Match the Pythagorean ratios to their intervals) 4/3

Perfect Fourth

(Match the Pythagorean ratios to their intervals) 3/2

Perfect Fifth

(Match the Pythagorean ratios to their intervals) 81/64

Major Third

Bower defines Western Music Theory as the tradition that attempts to reflect systematically about given ___________________ and apply these reflections to the _________________ and __________________ of musical repertoires.

musical phenomena; analysis; composition

What North African writer was instrumental in establishing the number of liberal arts at seven, as well as the canon of arts for the later Middle Ages?

Martianus Capella

(Match the list of liberal arts with its author) Grammar, Dialectic, Rhetoric, Geometry, Arithmetic, Astronomy, Harmony

Martianus (5th Century CE)

(Match the list of liberal arts with its author) Grammar, Rhetoric, Dialectic, Arithmetic, Geometry, Music, Astronomy, Medicine

Isidore (7th Century CE)

(Match the list of liberal arts with its author) Arithmetic, Music, Geometry, Astronomy

Boethius (6th Century CE)

(Match the list of liberal arts with its author) Grammar, Rhetoric, Dialectic, Arithmetic, Music, Geometry, Astronomy

Cassiodorus (6th Century CE)

(Match the list of liberal arts with its author) Grammar, Dialectic, Rhetoric, Geometry, Arithmetic, Astrology, Music, Medicine, Architecture

Varro (1st Century BCE)

In The Marriage of Philology and Mercury, Martianus Capella began a tradition of viewing the arts as intellectual disciplines that enabled the human mind to rise to the level of divine intellect. (True/False)

True

In his musical treatise, aptly titled ______________________, Augustine follows the _________________ tradition of ancient Greek musical thought.

De musica (On Music); Pythagorean

While Augustine focused on poetic and celestial ratios rather than strictly musical, he still left a lasting imprint on Western musical thought. What was his primary role in the preservation of musical theory?

He justified secular learning as important to Christian values

Who was the most prolific and influential scholar in the Platonic tradition of the early Middle Ages?

Boethius

(Boethius divided quantity into two genera): ____________ was discrete quantity, begins with a single, indivisible unit, and can ____________________________.

multitude; increase infinitely

(Boethius divided quantity into two genera): ____________________is a continuous quantity, represented by a line or shape, and can be ____________________________.

magnitude; infinitely divided

(Match the disciplines of the quadrivium to their definitions) considered immobile magnitudes

geometry

(Match the disciplines of the quadrivium to their definitions) investigated magnitudes in motion

astronomy

(Match the disciplines of the quadrivium to their definitions) examined number in ratios and proportions

music