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![Mixo-lydian b - b ¼ ¼ 2 ¼ ¼ 2 1
Lydian b*- b* ¼ 2 ¼ ¼ 2 1 ¼
Phrygian c - c 2 ¼ ¼ 2 1 ¼ ¼
Dorian e - e ¼ ¼ 2 1 ¼ ¼ 2
Hypo-lydian e*- e* ¼ 2 1 ¼ ¼ 2 ¼
Hypo-phrygian f - f 2 1 ¼ ¼ 2 ¼ ¼
Hypo-dorian a - a 1 ¼ ¼ 2 ¼ ¼ 2
On the Diatonic scale, according to the same writer, the species of an
Octave is distinguished by the places of the two semitones. Thus in
the first species, b-b, the semitones are the first and fourth intervals
(b-c and e-f): in the second, c-c, they are the third and the seventh,
and so on. He does not however say, as he does in the case of the
Enharmonic scale, that these species were known by the names of
the Keys. This statement is first made by Gaudentius (p. 20 Meib.), a
writer of unknown date. If we adopt it provisionally, the species of
the Diatonic octave will be as follows:
[Mixo-lydian] b - b ½ 1 1 ½ 1 1 1
[Lydian] c - c 1 1 ½ 1 1 1 ½
[Phrygian] d - d 1 ½ 1 1 1 ½ 1
[Dorian] e - e ½ 1 1 1 ½ 1 1
[Hypo-lydian] f - f 1 1 1 ½ 1 1 ½
[Hypo-phrygian] g - g 1 1 ½ 1 1 ½ 1
[Hypo-dorian] a - a 1 ½ 1 1 ½ 1 1](https://image.slidesharecdn.com/18225-250318084828-316cb52e/75/Operations-Management-Processes-and-Supply-Chains-11th-Edition-Krajewski-Test-Bank-26-2048.jpg)
![§ 26. The Ethos of the Genera and
Species.
Although the pitch of a musical composition—as these passages
confirm us in believing—was the chief ground of its ethical character,
it cannot be said that no other element entered into the case.
In the passage quoted above from Aristides Quintilianus (p. 13 Meib.)
it is said that ethos depends first on pitch (hetera êthê tois
oxyterois, hetera tois baryterois), and secondly on the moveable
notes, that is to say, on the genus. For that is evidently involved in
the words that follow: kai hetera men parypatoeidesin, hetera
de lichanoeidesin. By parypatoeideis and lichanoeideis he
means all the moveable notes (phthongoi pheromenoi): the first
are those which hold the place of Parhypatê in their tetrachord, viz.
the notes called Parhypatê or Tritê: the second are similarly the notes
called Lichanos or Paranêtê. These moveable notes, then, give an
ethos to the music because they determine the genus of the scale.
Regarding the particular ethos belonging to the different genera,
there is a statement of the same author (p. 111) to the effect that
the Diatonic is masculine and austere (arrhenôpon d' esti kai
austêroteron), the Chromatic sweet and plaintive (hêdiston te kai
goeron), the Enharmonic stirring and pleasing (diegertikon d' esti
touto kai êpion). The criticism doubtless came from some earlier
source.
Do we ever find ethos attributed to this or that species of the
Octave? I can find no passage in which this source of ethos is
indicated. Even Ptolemy, who is the chief authority (as we shall see)
for the value of the species, and who makes least of mere difference
of pitch, recognises only two forms of modulation in the course of a
melody, viz. change of genus and change of pitch [25].](https://image.slidesharecdn.com/18225-250318084828-316cb52e/75/Operations-Management-Processes-and-Supply-Chains-11th-Edition-Krajewski-Test-Bank-34-2048.jpg)
![archaic form of the letter[26]. The character , as Westphal shows, is
for , or delta with part of one side left out. Similarly the ancient ,
when the circle was incomplete, yielded the character C . The
crooked iota ( ) appears as . The two forms of lambda serve for
different notes, thus bringing the number of symbols up to fifteen.
Besides these there are two characters, and , which cannot be
derived in the same way from any alphabet. As they stand for the
lowest notes of the scale, they are probably an addition, later than
the rest of the system. At the upper end, again, the scale is extended
by the simple device of using the same characters for notes an
octave higher, distinguishing them in this use by an accent. The
original fifteen characters, with the letters from which they are
derived, and the corresponding notes in the modern musical scale,
are as follows:
These notes, it will be seen, compose two octaves of the Diatonic
scale, identical with the two octaves of the Greater Perfect System.
They may be regarded as answering to the white notes of the
modern keyboard,—those which form the complete scale in the so-
called 'natural' key.
The other notes, viz. those which are required not only in different
keys of the Diatonic scale, but also in all Enharmonic and Chromatic
scales, are represented by the same characters modified in some
simple way. Usually a character is turned half round backwards to
raise it by one small interval (as from Hypatê to Parhypatê), and
reversed to raise it by both (Hypatê to Lichanos). Thus the letter
epsilon, , stands for our c: and accordingly (
anestrammenon or hyption) stands for c*, and (
apestrammenon) for c ♯ . The Enharmonic scale c-c*-c ♯ -f is](https://image.slidesharecdn.com/18225-250318084828-316cb52e/75/Operations-Management-Processes-and-Supply-Chains-11th-Edition-Krajewski-Test-Bank-37-2048.jpg)
![therefore written , the two modifications of the letter
representing the two 'moveable' notes of the tetrachord. Similarly we
have the triads , , , ,
, , . As some letters do not admit of this kind
of differentiation, other methods are employed. Thus Δ is made to
yield the forms (for ) Δ: from H (or B) are obtained the forms
and : and from Z (or I]) the forms and . The
modifications of N are / and : those of are and .
The method of writing a Chromatic tetrachord is the same, except
that the higher of the two moveable notes is marked by a bar or
accent. Thus the tetrachord c c♯ d f is written .
In the Diatonic genus we should have expected that the original
characters would have been used for the tetrachords b c d e and e f
g a; and that in other tetrachords the second note, being a semitone
above the first, would have been represented by a reversed letter
(gramma apestrammenon). In fact, however, the Diatonic
Parhypatê and Tritê are written with the same character as the
Enharmonic. That is to say, the tetrachord b c d e is not written
, but : and d e ♭ f g is not , but
.
Let us now consider how this scheme of symbols is related to the
Systems already described and the Keys in which those Systems may
be set (tonoi eph' hôn tithemena ta systêmata melôdeitai).
The fifteen characters, it has been noticed, form two diatonic
octaves. It will appear on a little further examination that the scheme
must have been constructed with a view to these two octaves. The
successive notes are not expressed by the letters of the alphabet in
their usual order (as is done in the case of the vocal notes). The
highest note is represented by the first letter, A: and then the
remaining fourteen notes are taken in pairs, each with its octave: and](https://image.slidesharecdn.com/18225-250318084828-316cb52e/75/Operations-Management-Processes-and-Supply-Chains-11th-Edition-Krajewski-Test-Bank-38-2048.jpg)
![epigraphic record, or (2) that as a form of iota was still known—as
archaic forms must have been—from the older public inscriptions,
and was adopted by the inventor of the notation as being better
suited to his purpose than .
With regard to the place of origin of the notation the chief fact which
we have to deal with is the use of the character for lambda, which
is distinctive of the alphabet of Argos, along with the commoner form
. Westphal indeed asserts that both these forms are found in the
Argive alphabet. But the inscription (C. I. 1) which he quotes [27] for
really contains only in a slightly different form. We cannot
therefore say that the inventor of the notation derived it entirely from
the alphabet of Argos, but only that he shows an acquaintance with
that alphabet. This is confirmed by the fact that the form for iota
is not found at Argos. Probably therefore the inventor drew upon
more than one alphabet for his purpose, the Argive alphabet being
one.
The special fitness of the notation for the scales of the Enharmonic
genus may be regarded as a further indication of its date. We shall
see presently that that genus held a peculiar predominance in the
earliest period of musical theory—that, namely, which was brought to
an end by Aristoxenus.
If the author of the notation—or the second author, inventor of the
modified characters—was one of the musicians whose names have
come down to us, it would be difficult to find a more probable one
than that of Pronomus of Thebes. One of the most striking features
of the notation, at the time when it was framed, must have been the
adjustment of the keys. Even in the time of Aristoxenus, as we know
from the passage so often quoted, that adjustment was not universal.
But it is precisely what Pronomus of Thebes is said to have done for
the music of the flute (supra, p. 38). The circumstance that the
system was only used for instrumental music is at least in harmony
with this conjecture. If it is thought that Thebes is too far from Argos,
we may fall back upon the notice that Sacadas of Argos was the chief
composer for the flute before the time of Pronomus, [28] and](https://image.slidesharecdn.com/18225-250318084828-316cb52e/75/Operations-Management-Processes-and-Supply-Chains-11th-Edition-Krajewski-Test-Bank-42-2048.jpg)
![§ 29. Ptolemy's Scheme of Modes.
The first writer who takes the Species of the Octave as the basis of
the musical scales is the mathematician Claudius Ptolemaeus (fl. 140-
160 A.D.). In his Harmonics he virtually sets aside the scheme of
keys elaborated by Aristoxenus and his school, and adopts in their
place a system of scales answering in their main features to the
mediaeval Tones or Modes. The object of difference of key, he says,
is not that the music as a whole may be of a higher or lower pitch,
but that a melody may be brought within a certain compass. For this
purpose it is necessary to vary the succession of intervals (as a
modern musician does by changing the signature of the clef). If, for
example, we take the Perfect System (systêma ametabolon) in the
key of a minor—which is its natural key,—and transpose it to the key
of d minor, we do so, according to Ptolemy, not in order to raise the
general pitch of our music by a Fourth, but because we wish to have
a scale with b flat instead of b natural. The flattening of this note,
however, means that the two octaves change their species. They are
now of the species e-e. Thus, instead of transposing the Perfect
System into different keys, we arrive more directly at the desired
result by changing the species of its octaves. And as there are seven
possible species of the Octave, we obtain seven different Systems or
scales. From these assumptions it follows, as Ptolemy shows in some
detail, that any greater number of keys is useless. If a key is an
octave higher than another, it is superfluous because it gives us a
mere repetition of the same intervals [29].
If we interpose a key between (e.g.) the Hypo-dorian and the Hypo-
phrygian, it must give us over again either the Hypo-dorian or the
Hypo-phrygian scale [30]. Thus the fifteen keys of the Aristoxeneans
are reduced to seven, and these seven are not transpositions of a
single scale, but are all of the same pitch. See the table at the end of
the book.](https://image.slidesharecdn.com/18225-250318084828-316cb52e/75/Operations-Management-Processes-and-Supply-Chains-11th-Edition-Krajewski-Test-Bank-46-2048.jpg)
![With this scheme of Keys Ptolemy combined a new method of naming
the individual notes. The old method, by which a note was named
from its relative place in the Perfect System, must evidently have
become inconvenient. The Lydian Mesê, for example, was two tones
higher than the Dorian Mesê, because the Lydian scale as a whole
was two tones higher than the Dorian. But when the two scales were
reduced to the same compass, the old Lydian Mesê was no longer in
the middle of the scale, and the name ceased to have a meaning. It
is as though the term 'dominant' when applied to a Minor key were
made to mean the dominant of the relative Major key. On Ptolemy's
method the notes of each scale were named from their places in it.
The old names were used, Proslambanomenos for the lowest, Hypatê
Hypatôn for the next, and so on, but without regard to the intervals
between the notes. Thus there were two methods of naming, that
which had been in use hitherto, termed 'nomenclature according to
value' (onomasia kata dynamin), and the new method of naming
from the various scales, termed 'nomenclature according to position'
(onomasia kata thesin). The former was in effect a retention of
the Perfect System and the Keys: the latter put in their place a
scheme of seven different standard Systems.
In illustration of his theory Ptolemy gives tables showing in numbers
the intervals of the octaves used in the different keys and genera. He
shows two octaves in each key, viz. that from Hypatê Mesôn (kata
thesin) to Nêtê Diezeugmenôn (called the octave apo nêtês), and
that from Proslambanomenos to Mesê (the octave apo mesês). As
he also gives the divisions of five different 'colours' or varieties of
genus, the whole number of octaves is no less than seventy.
Ptolemy does not exclude difference of pitch altogether. The whole
instrument, he says, may be tuned higher or lower at pleasure [31].
Thus the pitch is treated by him as modern notation treats the
tempo, viz. as something which is not absolutely given, but has to be
supplied by the individual performer.
Although the language of Ptolemy's exposition is studiously
impersonal, it may be gathered that his reduction of the number of](https://image.slidesharecdn.com/18225-250318084828-316cb52e/75/Operations-Management-Processes-and-Supply-Chains-11th-Edition-Krajewski-Test-Bank-47-2048.jpg)
![keys from fifteen to seven was an innovation proposed by himself
[32]. If this is so, the rest of the scheme,—the elimination of the
element of pitch, and the 'nomenclature by position,'—must also be
due to him. Here, however, we find ourselves at issue with Westphal
and those who agree with him on the main question of the Modes.
According to Westphal the nomenclature by position is mentioned by
Aristoxenus, and is implied in at least one important passage of the
Aristotelian Problems. We have now to examine the evidence which
he adduces to support his contention.](https://image.slidesharecdn.com/18225-250318084828-316cb52e/75/Operations-Management-Processes-and-Supply-Chains-11th-Edition-Krajewski-Test-Bank-48-2048.jpg)
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- 5. 1 Copyright © 2016Pearson Education, Inc. Operations Management, 11e (Krajewski et al.) Chapter 7: Project Management 7.1 Defining and Organzing Projects 1) A project is an interrelated set of activities that has a definite starting and ending point. Answer: TRUE Reference: Defining and Organizing Projects Difficulty: Easy Keywords: project activities, start, end Learning Outcome: Describe the goals and stages of project management. AACSB: Application of Knowledge 2) Projects often cut across organizational lines. Answer: TRUE Reference: Defining and Organizing Projects Difficulty: Easy Keywords: project, organizational lines Learning Outcome: Describe the goals and stages of project management. AACSB: Application of Knowledge 3) Projects, and the application of project management, facilitate the implementation of operations strategy. Answer: TRUE Reference: Defining and Organizing Projects Difficulty: Easy Keywords: project management, operations strategy Learning Outcome: Describe the goals and stages of project management. AACSB: Application of Knowledge 4) Project managers should be able to organize a set of disparate activities. Answer: TRUE Reference: Defining and Organizing Projects Difficulty: Moderate Keywords: project manager, disparate activities Learning Outcome: Describe the goals and stages of project management. AACSB: Application of Knowledge 5) A pure project organizational structure houses the project in a specific functional area. Answer: FALSE Reference: Defining and Organizing Projects Difficulty: Moderate Keywords: pure project, functional structure Learning Outcome: Describe the goals and stages of project management. AACSB: Application of Knowledge
- 6. 2 Copyright © 2016Pearson Education, Inc. 6) Scope creep is one of the primary causes of project failure. Answer: TRUE Reference: Defining and Organizing Projects Difficulty: Moderate Keywords: scope creep, project failure Learning Outcome: Describe the goals and stages of project management. AACSB: Application of Knowledge 7) The project's objective statement should contain: A) slack time and activities. B) scope, time frame, and allocated resources. C) strengths and weaknesses of subcontractors. D) activities, completion times, and incentives. Answer: B Reference: Defining and Organizing Projects Difficulty: Moderate Keywords: project objective statement, scope Learning Outcome: Describe the goals and stages of project management. AACSB: Application of Knowledge 8) A project organization structure where team members are assigned to the project and work exclusively for the project manager is called: A) a matrix structure. B) a fixed structure. C) a pure project structure. D) a functional structure. Answer: C Reference: Defining and Organizing Projects Difficulty: Moderate Keywords: project, organizational structure Learning Outcome: Describe the goals and stages of project management. AACSB: Application of Knowledge 9) A(n) ________ is an interrelated set of activities that has a definite starting and ending point and that results in a unique outcome for a specific allocation of resources. Answer: project Reference: Defining and Organizing Projects Difficulty: Easy Keywords: project activities Learning Outcome: Describe the goals and stages of project management. AACSB: Application of Knowledge
- 7. 3 Copyright © 2016Pearson Education, Inc. 10) Heidi was part of a project team that retained their roles within the organization and was on loan to the project due to her technical expertise. In effect, she reported to two bosses, one in her functional area and also to the project manager. Heidi is operating within a(n) ________ organizational structure. Answer: matrix Reference: Defining and Organizing Projects Difficulty: Moderate Keywords: matrix Learning Outcome: Describe the goals and stages of project management. AACSB: Application of Knowledge 11) What are the primary responsibilities of a Project Manager? Briefly describe these responsibilities for a project manager whose team is purchasing a new machine and installing it in a manufacturing process. Answer: Best answers will include the following points, describing the manager's role in the purchase and installation of the new machine: 1. Facilitator: resolves conflicts; leads with a system view; blends project interaction, resources and deliverables with firm as a whole; 2. Communicator: informs senior management and other stakeholders of project's progress and need for additional resources; communicates with project team to achieve best performance; 3. Decision Maker: organize team meetings; define how team decisions will be made; determine how to communicate to senior management; make tough decisions if necessary. Reference: Defining and Organizing Projects Difficulty: Moderate Keywords: project manager, selecting Learning Outcome: Describe the goals and stages of project management. AACSB: Application of Knowledge 12) What characteristics should be considered when selecting project team members? Briefly describe these characteristics for members of a project team assigned to improve a teller's job in a bank. Answer: Best answers should include the following in the context on the job improvement project: 1. Technical Competence: capable of completing activities assigned to them; 2. Sensitivity: to interpersonal conflicts within the team; help mitigate these issues and any problems dealing with upper level management; 3. Dedication: capable of solving problems outside immediate expertise by involving others as needed; display persistence and initiative for completing the project in a timely fashion. Reference: Defining and Organizing Projects Difficulty: Moderate Keywords: project team member, selecting Learning Outcome: Describe the goals and stages of project management. AACSB: Application of Knowledge
- 8. 4 Copyright © 2016Pearson Education, Inc. 7.2 Constructing Project Networks 1) The work breakdown structure is a statement of all work that has to be completed. Answer: TRUE Reference: Constructing Project Networks Difficulty: Moderate Keywords: WBS, work breakdown structure Learning Outcome: Describe the goals and stages of project management. AACSB: Application of Knowledge 2) The network diagram is a planning method that is designed to depict the relationships between activities. Answer: TRUE Reference: Constructing Project Networks Difficulty: Moderate Keywords: network diagram, activities Learning Outcome: Describe the goals and stages of project management. AACSB: Application of Knowledge 3) A relationship that determines the sequence for undertaking activities is a precedence relationship. Answer: TRUE Reference: Constructing Project Networks Difficulty: Easy Keywords: precedence relationship Learning Outcome: Describe the goals and stages of project management. AACSB: Application of Knowledge 4) In a network diagram, an activity: A) is the largest unit of work effort consuming both time and resources that a project manager can schedule and control. B) is the smallest unit of work effort consuming both time and resources that a project manager can schedule and control. C) should always be something the company has had experience with. D) must always have a single, precise estimate for the time duration. Answer: B Reference: Constructing Project Networks Difficulty: Moderate Keywords: activity, smallest unit of work Learning Outcome: Describe the goals and stages of project management. AACSB: Application of Knowledge
- 9. 5 Copyright © 2016Pearson Education, Inc. 5) Activity times for a project are estimated by all but which of the following methods? A) the use of dowsing rods. B) managerial opinions based on similar prior experiences C) statistical methods based on actual past experience D) estimates using learning curve models to improve replications and estimate accuracy Answer: A Reference: Constructing Project Networks Difficulty: Moderate Keywords: activity times, estimating activity times Learning Outcome: Describe the goals and stages of project management. AACSB: Application of Knowledge 6) The ________ is a statement of all work that has to be completed. Answer: work breakdown structure (WBS) Reference: Constructing Project Networks Difficulty: Moderate Keywords: WBS, work breakdown structure Learning Outcome: Describe the goals and stages of project management. AACSB: Application of Knowledge 7) ________ determines the sequence for undertaking activities. Answer: Precedence relationship Reference: Constructing Project Networks Difficulty: Moderate Keywords: precedence relationship, sequence of activities Learning Outcome: Describe the goals and stages of project management. AACSB: Application of Knowledge 8) Following the project defining and organizing phase, project planning involves five steps. List and briefly describe these five planning steps as applied to writing a term paper for an Operations Management class. Answer: The following points should be included in the best answers: 1. Define the work breakdown structure: develop a list of all work to be completed on the project; 2. Diagram the network: develop a PERT/CPM diagram showing all activities and precedence requirements for the project; 3. Develop the schedule: define the project's critical path, duration, and earliest and latest start and finish times for each activity; 4. Analyze cost–time trade-offs: determine normal time and costs for the project, as well as crash time and costs; using project crashing techniques, find a minimum cost schedule for completing the project; 5. Assess project risks: develop a risk management plan, including such areas as strategic fit, service/product attributes, team capabilities and operations risks. Reference: Constructing Project Networks Difficulty: Moderate Keywords: project planning, steps Learning Outcome: Describe the goals and stages of project management. AACSB: Application of Knowledge
- 10. 6 Copyright © 2016Pearson Education, Inc. 7.3 Developing the Project Schedule 1) A critical path is any sequence of activities between a project's start and finish. Answer: FALSE Reference: Developing the Project Schedule Difficulty: Moderate Keywords: critical path activities Learning Outcome: Describe the goals and stages of project management. AACSB: Application of Knowledge 2) The earliest start time is never the same as the latest start time. Answer: FALSE Reference: Developing the Project Schedule Difficulty: Easy Keywords: earliest start time, latest start time Learning Outcome: Describe the goals and stages of project management. AACSB: Analytical Thinking 3) To obtain the latest start and latest finish time in a network diagram, we must work forward through the network. Answer: FALSE Reference: Developing the Project Schedule Difficulty: Moderate Keywords: latest start time, latest finish time Learning Outcome: Describe the goals and stages of project management. AACSB: Application of Knowledge 4) A Gantt chart is a project schedule that superimposes project activities on a time line. Answer: TRUE Reference: Developing the Project Schedule Difficulty: Moderate Keywords: Gantt chart, project schedule Learning Outcome: Describe the goals and stages of project management. AACSB: Application of Knowledge 5) A project has three paths. A-B-C has a length of 25 days. A-D-C has a length of 15 days. Finally, A-E-C has a length of 20 days. Which one of the following statements is TRUE? A) A-D-C is the critical path. B) A-B-C has the most slack. C) The expected duration of this project is 25 days. D) The expected duration of this project is 25 + 15 + 20 = 60 days. Answer: C Reference: Developing the Project Schedule Difficulty: Moderate Keywords: project, duration Learning Outcome: Describe the goals and stages of project management. AACSB: Analytical Thinking
- 11. 7 Copyright © 2016Pearson Education, Inc. 6) The earliest start time for an activity is equal to the: A) smallest earliest finish time of all of its immediate predecessors. B) largest earliest finish time of all of its immediate predecessors. C) smallest late start time of any of its immediate predecessors. D) largest late finish time of all of its immediate predecessors. Answer: B Reference: Developing the Project Schedule Difficulty: Moderate Keywords: activity, earliest start time Learning Outcome: Describe the goals and stages of project management. AACSB: Analytical Thinking 7) Assume that activity G has the following times: Early start time = 7 days Early finish time = 13 days Late start time = 15 days Late finish time = 21 days Which of the following statements is TRUE about activity G? A) Activity G takes 14 days to complete. B) Activity G has a slack time of 8 days. C) Activity G is on the critical path. D) Activity G takes 2 days to complete. Answer: B Reference: Developing the Project Schedule Difficulty: Moderate Keywords: activity slack Learning Outcome: Describe the goals and stages of project management. AACSB: Analytical Thinking 8) Activity slack is defined as: A) latest start time minus earliest start time. B) earliest start time minus latest start time. C) earliest finish time minus latest finish time. D) latest finish time minus earliest start time. Answer: A Reference: Developing the Project Schedule Difficulty: Moderate Keywords: activity slack, latest start time, earliest start time Learning Outcome: Describe the goals and stages of project management. AACSB: Analytical Thinking
- 12. 8 Copyright © 2016Pearson Education, Inc. 9) Which one of the following best describes the critical path of a PERT/CPM network? A) the sequence of activities between a project's start and finish that takes the longest time to complete B) the sequence of activities between a project's start and finish that has the maximum amount of activity slack C) the set of activities that has no precedence relationships D) the sequence of activities that has the lowest normal activity cost Answer: A Reference: Developing the Project Schedule Difficulty: Moderate Keywords: critical path Learning Outcome: Describe the goals and stages of project management. AACSB: Analytical Thinking Fig. 7.1 10) For the network shown in Fig. 7.1, which of the following is the critical path? A) ABCDEF B) ABEF C) ACDF D) ACEF Answer: C Reference: Developing the Project Schedule Difficulty: Easy Keywords: activity network, critical path Learning Outcome: Describe the goals and stages of project management. AACSB: Analytical Thinking
- 13. 9 Copyright © 2016Pearson Education, Inc. 11) For the network shown in Fig. 7.1, what is the project duration? A) 6 B) 15 C) 13 D) 14 Answer: B Reference: Developing the Project Schedule Difficulty: Easy Keywords: activity network, critical path, duration Learning Outcome: Describe the goals and stages of project management. AACSB: Analytical Thinking
- 14. 10 Copyright © 2016Pearson Education, Inc. Figure to accompany Table 7.1 Table 7.1 Activity Activity Time Earliest Start Earliest Finish Latest Start Latest Finish Slack A 2 0 0 2 0 B 1 2 3 3 4 1 C 3 2 5 2 5 0 D 7 3 10 4 11 E 3 5 8 11 3 F 5 11 5 11 0 G 4 11 15 11 15 0 12) Using the information shown in Table 7.1, what is the slack time for activity D? A) 1 B) 4 C) 6 D) 7 Answer: A Reference: Developing the Project Schedule Difficulty: Easy Keywords: activity, network, critical path, activity slack Learning Outcome: Describe the goals and stages of project management. AACSB: Analytical Thinking
- 15. 11 Copyright © 2016Pearson Education, Inc. 13) Using the information shown in Table 7.1, what is the earliest finish time for activity A? A) 0 B) 2 C) 3 D) 4 Answer: B Reference: Developing the Project Schedule Difficulty: Easy Keywords: activity network, critical path, earliest finish Learning Outcome: Describe the goals and stages of project management. AACSB: Analytical Thinking 14) Using the information shown in Table 7.1, what is the latest start time for activity E? A) 2 B) 3 C) 5 D) 8 Answer: D Reference: Developing the Project Schedule Difficulty: Easy Keywords: activity network, critical path, latest start Learning Outcome: Describe the goals and stages of project management. AACSB: Analytical Thinking 15) Using the information shown in Table 7.1, what is the activity time for activity F? A) 5 B) 11 C) 6 D) 1 Answer: C Reference: Developing the Project Schedule Difficulty: Easy Keywords: activity network, critical path, activity time Learning Outcome: Describe the goals and stages of project management. AACSB: Analytical Thinking 16) Refer to the Figure to accompany Table 7.1. Which one of the following is the critical path? A) ABDG B) ABEG C) ACEG D) ACFG Answer: D Reference: Developing the Project Schedule Difficulty: Easy Keywords: activity network, critical path Learning Outcome: Describe the goals and stages of project management. AACSB: Analytical Thinking
- 16. 12 Copyright © 2016Pearson Education, Inc. 17) Using the information shown in Table 7.1, what is the project duration? A) 15 B) 14 C) 12 D) 10 Answer: A Reference: Developing the Project Schedule Difficulty: Easy Keywords: activity network, critical path, duration Learning Outcome: Describe the goals and stages of project management. AACSB: Analytical Thinking 18) Fig. 7.2 Which one of the following statements regarding Figure 7.2 is TRUE? A) Activity S cannot finish until activity T finishes. B) Activity T cannot begin until activity U is completed. C) Activity U cannot begin until activities S and T have been completed. D) Activity V cannot begin until activity S has been completed. Answer: C Reference: Developing the Project Schedule Difficulty: Moderate Keywords: activity precedence Learning Outcome: Describe the goals and stages of project management. AACSB: Application of Knowledge 19) Which one of the following conditions violates the assumptions of PERT/CPM networks? A) Some activities can have zero variance. B) Costs increase linearly as activity time is reduced below its normal time. C) Two activities tied together by an arc are overlapping and can be worked on simultaneously. D) There can be more than one critical path in a network. Answer: C Reference: Developing the Project Schedule Difficulty: Moderate Keywords: assumption, PERT and CPM networks Learning Outcome: Describe the goals and stages of project management. AACSB: Application of Knowledge
- 17. 13 Copyright © 2016Pearson Education, Inc. 20) The ________ is the sequence of activities between a project's start and finish that takes the longest time to complete. Answer: critical path Reference: Developing the Project Schedule Difficulty: Moderate Keywords: critical path Learning Outcome: Describe the goals and stages of project management. AACSB: Application of Knowledge 21) ________ is the maximum length of time that an activity can be delayed without delaying the entire project. Answer: Activity slack Reference: Developing the Project Schedule Difficulty: Moderate Keywords: activity slack Learning Outcome: Describe the goals and stages of project management. AACSB: Application of Knowledge 22) Explain the importance of the critical path in project management. Answer: The critical path of activities determines the time duration of the project. Any slippage along the critical path means the project will be delayed. The critical path also defines the activities requiring the team's attention and focus to assure timely and cost effective completion of the project. Reference: Developing the Project Schedule Difficulty: Moderate Keywords: project critical path Learning Outcome: Describe the goals and stages of project management. AACSB: Application of Knowledge 23) Why do managers want to know the slack of activities? Answer: Managers monitor activity slack reports to identify activities that have fallen behind schedule or are dangerously close to doing so. Also, activities with large amounts of slack might afford a reduction in resources so that other activities behind schedule can catch up. Reference: Developing the Project Schedule Difficulty: Moderate Keywords: activity slack Learning Outcome: Describe the goals and stages of project management. AACSB: Application of Knowledge
- 18. 14 Copyright © 2016Pearson Education, Inc. 24) Draw the network corresponding to the following information. Also, complete the table, identify the critical path, and specify project completion time. Activity Immediate Predecessor(s) Time (Weeks) A --- 3 B --- 4 C A 6 D B 9 E B 6 F C, D 6 G D, E 8 H G, F 9 Activity Earliest Start Earliest Finish Latest Start Latest Finish Slack A B C D E F G H Answer:
- 19. 15 Copyright © 2016Pearson Education, Inc. Activity Earliest Start Earliest Finish Latest Start Latest Finish Slack A 0 3 6 9 6 B 0 4 0 4 0 C 3 9 9 15 6 D 4 13 4 13 0 E 4 10 7 13 3 F 13 19 15 21 2 G 13 21 13 21 0 H 21 30 21 30 0 Critical path is B—D—G—H, and project completion time is 30 weeks. Reference: Developing the Project Schedule Difficulty: Moderate Keywords: early and late start and finish times, critical path, completion time Learning Outcome: Describe the goals and stages of project management. AACSB: Analytical Thinking
- 20. 16 Copyright © 2016Pearson Education, Inc. 25) Consider a project that consists of three consecutive activities of equal length as shown in the network diagram. The project manager would like to complete the project as quickly as possible and realizes that the diagram's logic is misleading. Instead of waiting until activity A is completed before activity B can begin, he can actually begin activity B once activity A has begun. The same reasoning holds for the relationship between activity B and activity C. The project manager decides to divide each activity in half, a technique known as "laddering". The second diagram shows the new network logic. In this diagram, activity A is divided into activity A1 and A2 where A1 must be finished before A2 can begin and before B1 can begin. The manager still isn't satisfied with the completion time of the project. Derive an expression or draw a diagram that demonstrates the fastest possible completion time of the project. Answer: The original length of the project is A+B+C. When laddering is performed the first time, the project length becomes A1+B1+C1+C2; this is because A2 can be performed concurrently with B1 and B2 can be performed concurrently with C1. Alternatively, you can choose to focus on the completion of activity A and indicate that the new project length is A1 + A2 + B2 + C2 (or even A1 + B1 B2 + C2). If the activities are divided again, the project length will be A1 + B1 + C1 + C2 + C3 + C4; because A2, A3, A4, B2, B3, and B4 can be performed concurrently with other activities. In general, the project can be viewed as the length of C plus the waiting time while completing the length of subdivided activities A and B. As the number of iterations of laddering these activities becomes large, the length of sub-activity A1 and B1 becomes small, effectively reducing project length to the length of activity C. Expressed mathematically where P is the project length: Without laddering P = A + B + C 1st ladder P = + + C 2nd ladder P = + + C Subsequent P = = C A Gantt chart showing two halvings of the activities is shown below. The three activities were 4 days long before laddering and are now are effectively twelve activities that are each one day in length.
- 21. 17 Copyright © 2016Pearson Education, Inc. Reference: Developing the Project Schedule Difficulty: Hard Keywords: critical path, project length, activity crashing Learning Outcome: Describe the goals and stages of project management. AACSB: Analytical Thinking
- 22. 18 Copyright © 2016Pearson Education, Inc. 26) Phoebe B. Beebee is constructing a canal for the annual canoe races and has identified eleven activities that are required to complete this important project. She calculated early and late start times and early and late finish times but spilled coffee all over her printout. Use the remaining information to reconstruct the table for Phoebe B. Beebee and her new canoe canal. Activity Predecessor Length Early Start Late Start Early Finish Late Finish A -- 12 B A 20 C A D B, E 42 E C 28 42 F E 42 50 G D 53 53 H G 70 I G 72 J F 4 K H, I, J 81 91 Answer: The completed table appears below: Activity Predecessor Length Early Start Late Start Early Finish Late Finish A -- 12 0 0 12 12 B A 20 12 22 32 42 C A 16 12 12 28 28 D B, E 11 42 42 53 53 E C 14 28 28 42 42 F E 8 42 69 50 77 G D 17 53 53 70 70 H G 11 70 70 81 81 I G 9 70 72 79 81 J F 4 50 77 54 81 K H, I, J 10 81 81 91 91 Reference: Developing the Project Schedule Difficulty: Hard Keywords: critical path, network, early and late start and finish times Learning Outcome: Describe the goals and stages of project management. AACSB: Analytical Thinking
- 23. 19 Copyright © 2016Pearson Education, Inc. 7.4 Analyzing Cost-Time Trade-Offs 1) The normal cost is the amount of money it normally takes to complete an activity faster than its normal time. Answer: FALSE Reference: Analyzing Cost-Time Trade-Offs Difficulty: Easy Keywords: normal cost, activity time, normal time Learning Outcome: Describe the goals and stages of project management. AACSB: Application of Knowledge 2) A project manager should stop crashing a project if the time budget has been met or if the crash costs have exceeded the savings in indirect and penalty costs. Answer: TRUE Reference: Analyzing Cost-Time Trade-Offs Difficulty: Moderate Keywords: crash cost, penalty costs, indirect costs Learning Outcome: Describe the goals and stages of project management. AACSB: Application of Knowledge Table 7.4 Activity Predecessor Time(weeks) A -- 8 B A 6 C -- 4 D C 9 E A 11 F B 3 G D, E, F 1 3) Using Table 7.4, what is the earliest completion time for this project? A) 18 weeks B) 19 weeks C) 20 weeks D) 21 weeks Answer: C Reference: Analyzing Cost-Time Trade-Offs Difficulty: Moderate Keywords: completion time Learning Outcome: Describe the goals and stages of project management. AACSB: Analytical Thinking
- 24. 20 Copyright © 2016Pearson Education, Inc. 4) Using Table 7.4, what is the largest amount of slack that any activity in the project has? A) zero weeks B) two weeks C) four weeks D) six weeks Answer: D Reference: Analyzing Cost-Time Trade-Offs Difficulty: Moderate Keywords: activity slack Learning Outcome: Describe the goals and stages of project management. AACSB: Analytical Thinking 5) Using Table 7.4, what is the minimum number of activities that would have to be delayed to cause an increase in the project's earliest completion date? A) one activity B) two activities C) three activities D) four or more activities Answer: A Reference: Analyzing Cost-Time Trade-Offs Difficulty: Moderate Keywords: activity delay, earliest completion time Learning Outcome: Describe the goals and stages of project management. AACSB: Analytical Thinking 6) Using Table 7.4, what is the minimum number of activities that would have to be crashed to cause a decrease in the project's earliest completion date? A) one activity B) two activities C) three activities D) four or more activities Answer: A Reference: Analyzing Cost-Time Trade-Offs Difficulty: Moderate Keywords: crashing an activity, earliest completion time Learning Outcome: Describe the goals and stages of project management. AACSB: Analytical Thinking
- 25. Another Random ScribdDocument with Unrelated Content
- 26. Mixo-lydian b -b ¼ ¼ 2 ¼ ¼ 2 1 Lydian b*- b* ¼ 2 ¼ ¼ 2 1 ¼ Phrygian c - c 2 ¼ ¼ 2 1 ¼ ¼ Dorian e - e ¼ ¼ 2 1 ¼ ¼ 2 Hypo-lydian e*- e* ¼ 2 1 ¼ ¼ 2 ¼ Hypo-phrygian f - f 2 1 ¼ ¼ 2 ¼ ¼ Hypo-dorian a - a 1 ¼ ¼ 2 ¼ ¼ 2 On the Diatonic scale, according to the same writer, the species of an Octave is distinguished by the places of the two semitones. Thus in the first species, b-b, the semitones are the first and fourth intervals (b-c and e-f): in the second, c-c, they are the third and the seventh, and so on. He does not however say, as he does in the case of the Enharmonic scale, that these species were known by the names of the Keys. This statement is first made by Gaudentius (p. 20 Meib.), a writer of unknown date. If we adopt it provisionally, the species of the Diatonic octave will be as follows: [Mixo-lydian] b - b ½ 1 1 ½ 1 1 1 [Lydian] c - c 1 1 ½ 1 1 1 ½ [Phrygian] d - d 1 ½ 1 1 1 ½ 1 [Dorian] e - e ½ 1 1 1 ½ 1 1 [Hypo-lydian] f - f 1 1 1 ½ 1 1 ½ [Hypo-phrygian] g - g 1 1 ½ 1 1 ½ 1 [Hypo-dorian] a - a 1 ½ 1 1 ½ 1 1
- 27. § 24. Relationof the Species to the Keys. Looking at the octaves which on our key-board, as on the Greek scale, exhibit the several species, we cannot but be struck with the peculiar relation in which they stand to the Keys. In the tables given above the keys stand in the order of their pitch, from the Mixo-lydian down to the Hypo-dorian: the species of the same names follow the reverse order, from b-b upwards to a-a. This, it is obvious, cannot be an accidental coincidence. The two uses of this famous series of names cannot have originated independently. Either the naming of the species was founded on that of the keys, or the converse relation obtained between them. Which of these two uses, then, was the original and which the derived one? Those who hold that the species were the basis of the ancient Modes or harmoniai must regard the keys as derivative. Now Aristoxenus tells us, in one of the passages just quoted, that the seven species had long been recognised by theorists. If the scheme of keys was founded upon the seven species, it would at once have been complete, both in the number of the keys and in the determination of the intervals between them. But Aristoxenus also tells us that down to his time there were only six keys,—one of them not yet generally recognised,—and that their relative pitch was not settled. Evidently then the keys, which were scales in practical use, were still incomplete when the species of the Octave had been worked out in the theory of music. If on the other hand we regard the names Dorian, &c. as originally applied to keys, we have only to suppose that these names were extended to the species after the number of seven keys had been completed. This supposition is borne out by the fact that Aristoxenus, who mentions the seven species as well known, does not give them names, or connect them with the keys. This step was apparently
- 28. taken by somefollower of Aristoxenus, who wished to connect the species of the older theorists with the system of keys which Aristoxenus had perfected. The view now taken of the seven species is supported by the whole treatment of musical scales (systêmata) as we find it in Aristoxenus. That treatment from first to last is purely abstract and theoretical. The rules which Aristoxenus lays down serve to determine the sequence of intervals, but are not confined to scales of any particular compass. His Systems, accordingly, are not scales in practical use: they are parts taken anywhere on an ideal unlimited scale. And the seven species of the Octave are regarded by Aristoxenus as a scheme of the same abstract order. They represent the earlier teaching on which he had improved. He condemned that teaching for its want of generality, because it was confined to the compass of the Octave and to the Enharmonic genus, and also because it rested on no principles that would necessarily limit the species of the Octave to seven. On the other hand the diagrams of the earlier musicians were unscientific, in the opinion of Aristoxenus, on the ground that they divided the scale into a succession of quarter-tones. Such a division, he urged, is impossible in practice and musically wrong (ekmeles). All this goes to show that the earlier treatment of Systems, including the seven Species, had the same theoretical character as his own exposition. The only System which he recognises for practical purposes is the old standard octave, from Hypatê to Nêtê: and that System, with the enlargements which turned it into the Perfect System, kept its ground with all writers of the Aristoxenean school. Even in the accounts of the pseudo-Euclid and the later writers, who treat of the Species of the Octave under the names of the Keys, there is much to show that the species existed chiefly or wholly in musical theory. The seven species of the Octave are given along with the three species of the Fourth and the four species of the Fifth, neither of which appear to have had any practical application. Another indication of this may be seen in the seventh or Hypo-dorian species, which was also called Locrian and Common (ps. Eucl. p. 16 Meib.). Why should this species have more than one name? In the Perfect
- 29. System it issingular in being exemplified by two different octaves, viz. that from Proslambanomenos to Mesê, and that from Mesê to Nêtê Hyperbolaiôn. Now we have seen that the higher the octave which represents a species, the lower the key of the same name. In this case, then, the upper of the two octaves answers to the Hypo- dorian key, and the lower to the Locrian. But if the species has its two names from these two keys, it follows that the names of the species are derived from the keys. The fact that the Hypo-dorian or Locrian species was also called Common is a further argument to the same purpose. It was doubtless 'common' in the sense that it characterised the two octaves which made up the Perfect System. Thus the Perfect System was recognised as the really important scale. Another consideration, which has been overlooked by Westphal and those who follow him, is the difference between the species of the Octave in the several genera, especially the difference between the Diatonic and the Enharmonic. This is not felt as a difficulty with all the species. Thus the so-called Dorian octave e-e is in the Enharmonic genus e e* f a b b* c e, a scale which may be regarded as the Diatonic with g and d omitted, and the semitones divided. But the Phrygian d-d cannot pass in any such way into the Enharmonic Phrygian c e e* f a b b* c, which answers rather to the Diatonic scale of the species c-c (the Lydian). The scholars who connect the ancient Modes with the species generally confine themselves to octaves of the Diatonic genus. In this they are supported by later Greek writers —notably, as we shall see, by Ptolemy—and by the analogy of the mediaeval Modes or Tones. But on the other side we have the repeated complaints of Aristoxenus that the earlier theorists confined themselves to Enharmonic octave scales. We have also the circumstance that the writer or compiler of the pseudo-Euclidean treatise, who is our earliest authority for the names of the species, gives these names for the Enharmonic genus only. Here, once more, we feel the difference between theory and practice. To a theorist there is no great difficulty in the terms Diatonic Phrygian and Enharmonic Phrygian meaning essentially different things. But the
- 30. 'Phrygian Mode' inpractical music must have been a tolerably definite musical form.
- 31. § 25. TheEthos of Music. From Plato and Aristotle we have learned some elements of what may be called the gamut of sensibility. Between the higher keys which in Greece, as in Oriental countries generally, were the familiar vehicle of passion, especially of the passion of grief, and the lower keys which were regarded, by Plato at least, as the natural language of ease and license, there were keys expressive of calm and balanced states of mind, free from the violent extremes of pain and pleasure. In some later writers on music we find this classification reduced to a more regular form, and clothed in technical language. We find also, what is still more to our purpose, an attempt to define more precisely the musical forms which answered to the several states of temper or emotion. Among the writers in question the most instructive is Aristides Quintilianus. He discusses the subject of musical ethos under the first of the usual seven heads, that which deals with sounds or notes (peri phthongôn). Among the distinctions to be drawn in regard to notes he reckons that of ethos: the ethos of notes, he says, is different as they are higher or lower, and also as they are in the place of a Parhypatê or in the place of a Lichanos (p. 13 Meib. hetera gar êthê tois oxyterois, hetera tois baryterois epitrechei, kai hetera men parypatoeidesin, hetera de lichanoeidesin). Again, under the seventh head, that of melopoiia or composition, he treats of the 'regions of the voice' (topoi tês phônês). There are three kinds of composition, he tells us (p. 28), viz. that which is akin to Hypatê (hypatoeidês), that which is akin to Mesê (mesoeidês), and that which is akin to Nêtê (nêtoeidês). The first part of the art of composition is the choice (lêpsis) which the musician is able to make of the region of the voice to be employed (lêpsis men di' hês heuriskein tô mousikô perigignetai apo poiou tês phônês to systêma topou poiêteon, poteron hypatoeidous ê tôn loipôn
- 32. tinos). He thenproceeds to connect these regions, or different parts of the musical scale, with different branches of lyrical poetry. 'There are three styles of musical composition (tropoi tês melopoiias), viz. the Nomic, the Dithyrambic, and the Tragic; and of these the Nomic is netoid, the Dithyrambic is mesoid, and the Tragic is hypatoid.... They are called styles (tropoi) because according to the melody adopted they express the ethos of the mind. Thus it happens that composition (melopoiia) may differ in genus, as Enharmonic, Chromatic: in System, as Hypatoid, Mesoid, Netoid: in key, as Dorian, Phrygian: in style, as Nomic, Dithyrambic: in ethos, as we call one kind of composition "contracting" (systaltikê), viz. that by which we move painful feelings; another "expanding" (diastaltikê), that by which we arouse the spirit (thymos); and another "middle" (mesê), that by which we bring round the soul to calmness.' This passage does not quite explicitly connect the three kinds of ethos—the diastaltic, the systaltic, the intermediate—with the three regions of the voice; but the connexion was evidently implied, and is laid down in express terms in the pseudo-Euclidean Introductio (p. 21 Meib.). According to this Aristoxenean writer, 'the diastaltic ethos of musical composition is that which expresses grandeur and manly elevation of soul (megaloprepeia kai diarma psychês andrôdes), and heroic actions; and these are employed by tragedy and all poetry that approaches the tragic type. The systaltic ethos is that by which the soul is brought down into a humble and unmanly frame; and such a disposition will be fitting for amatory effusions and dirges and lamentations and the like. And the hesychastic or tranquilly disposed ethos (hêsychastikon êthos) of musical composition is that which is followed by calmness of soul and a liberal and peaceful disposition: and this temper will fit hymns, paeans, laudations, didactic poetry and the like.' It appears then that difference in the 'place' (topos) of the notes employed in a composition—difference, that is to say, of pitch—was the element which chiefly determined its ethos, and (by consequence) which distinguished the music appropriate to the several kinds of lyrical poetry.
- 33. A slightly differentversion of this piece of theory is preserved in the anonymous treatise edited by Bellermann (§§ 63, 64), where the 'regions of the voice' are said to be four in number, viz. the three already mentioned, and a fourth which takes its name from the tetrachord Hyperbolaiôn (topos hyperboloeidês). In the same passage the boundaries of the several regions are laid down by reference to the keys. 'The lowest or hypatoid region reaches from the Hypo-dorian Hypatê Mesôn to the Dorian Mesê; the intermediate or mesoid region from the Phrygian Hypatê Mesôn to the Lydian Mesê; the netoid region from the Lydian Mesê to the Nêtê Synemmenôn; the hyperboloid region embracing all above the last point.' The text of this passage is uncertain; but the general character of the topoi or regions of the voice is clearly enough indicated. The three regions are mentioned in the catechism of Bacchius (p. 11 Meib.): topous (MSS. tropous) de tês phônês posous legomen einai? treis. tinas? toutous; oxyn, meson, baryn. The varieties of ethos also appear (p. 14 Meib.): hê de metabolê kata êthos? hotan ek tapeinou eis megaloprepes; ê ex hêsychou kai synnou eis parakekinêkos. 'What is change of ethos? when a change is made from the humble to the magnificent; or from the tranquil and sober to violent emotion.' When we compare the doctrine of musical ethos as we find it in these later writers with the indications to be gathered from Plato and Aristotle, the chief difference appears to be that we no longer hear of the ethos of particular modes, but only of that of three or (at the most) four portions of the scale. The principle of the division, it is evident, is simply difference of pitch. But if that was the basis of the ethical effect of music in later times, the circumstance goes far to confirm us in the conclusion that it was the pitch of the music, rather than any difference in the succession of the intervals, that principally determined the ethical character of the older modes.
- 34. § 26. TheEthos of the Genera and Species. Although the pitch of a musical composition—as these passages confirm us in believing—was the chief ground of its ethical character, it cannot be said that no other element entered into the case. In the passage quoted above from Aristides Quintilianus (p. 13 Meib.) it is said that ethos depends first on pitch (hetera êthê tois oxyterois, hetera tois baryterois), and secondly on the moveable notes, that is to say, on the genus. For that is evidently involved in the words that follow: kai hetera men parypatoeidesin, hetera de lichanoeidesin. By parypatoeideis and lichanoeideis he means all the moveable notes (phthongoi pheromenoi): the first are those which hold the place of Parhypatê in their tetrachord, viz. the notes called Parhypatê or Tritê: the second are similarly the notes called Lichanos or Paranêtê. These moveable notes, then, give an ethos to the music because they determine the genus of the scale. Regarding the particular ethos belonging to the different genera, there is a statement of the same author (p. 111) to the effect that the Diatonic is masculine and austere (arrhenôpon d' esti kai austêroteron), the Chromatic sweet and plaintive (hêdiston te kai goeron), the Enharmonic stirring and pleasing (diegertikon d' esti touto kai êpion). The criticism doubtless came from some earlier source. Do we ever find ethos attributed to this or that species of the Octave? I can find no passage in which this source of ethos is indicated. Even Ptolemy, who is the chief authority (as we shall see) for the value of the species, and who makes least of mere difference of pitch, recognises only two forms of modulation in the course of a melody, viz. change of genus and change of pitch [25].
- 36. § 27. TheMusical Notation. As the preceding argument turns very much upon the practical importance of the scale which we have been discussing, first as the single octave from the original Hypatê to Nêtê, then in its enlarged form as the Perfect System, it may be worth while to show that some such scale is implied in the history of the Greek musical notation. The use of written characters (sêmeia) to represent the sounds of music appears to date from a comparatively early period in Greece. In the time of Aristoxenus the art of writing down a melody (parasêmantikê) had come to be considered by some persons identical with the science of music (harmonikê),—an error which Aristoxenus is at some pains to refute. It is true that the authorities from whom we derive our knowledge of the Greek notation are post- classical. But the characters themselves, as we shall presently see, furnish sufficient evidence of their antiquity. The Greek musical notation is curiously complicated. There is a double set of characters, one for the note assigned to the singer, the other for those of the lyre or other instrument. The notes for the voice are obviously derived from the letters of the ordinary Ionic alphabet, multiplied by the use of accents and other diacritical marks. The instrumental notes were first explained less than thirty years ago by Westphal. In his work Harmonik und Melopöie der Griechen (c. viii Die Semantik) he showed, in a manner as conclusive as it is ingenious, that they were originally taken from the first fourteen letters of an alphabet of archaic type, akin to the alphabets found in certain parts of Peloponnesus. Among the letters which he traces, and which point to this conclusion, the most-significant are the digamma, the primitive crooked iota , and two forms of lambda, and , the latter of which is peculiar to the alphabet of Argos. Of the other characters , which stands for alpha, is best derived from the archaic form . For beta we find , which may come from an
- 37. archaic form ofthe letter[26]. The character , as Westphal shows, is for , or delta with part of one side left out. Similarly the ancient , when the circle was incomplete, yielded the character C . The crooked iota ( ) appears as . The two forms of lambda serve for different notes, thus bringing the number of symbols up to fifteen. Besides these there are two characters, and , which cannot be derived in the same way from any alphabet. As they stand for the lowest notes of the scale, they are probably an addition, later than the rest of the system. At the upper end, again, the scale is extended by the simple device of using the same characters for notes an octave higher, distinguishing them in this use by an accent. The original fifteen characters, with the letters from which they are derived, and the corresponding notes in the modern musical scale, are as follows: These notes, it will be seen, compose two octaves of the Diatonic scale, identical with the two octaves of the Greater Perfect System. They may be regarded as answering to the white notes of the modern keyboard,—those which form the complete scale in the so- called 'natural' key. The other notes, viz. those which are required not only in different keys of the Diatonic scale, but also in all Enharmonic and Chromatic scales, are represented by the same characters modified in some simple way. Usually a character is turned half round backwards to raise it by one small interval (as from Hypatê to Parhypatê), and reversed to raise it by both (Hypatê to Lichanos). Thus the letter epsilon, , stands for our c: and accordingly ( anestrammenon or hyption) stands for c*, and ( apestrammenon) for c ♯ . The Enharmonic scale c-c*-c ♯ -f is
- 38. therefore written ,the two modifications of the letter representing the two 'moveable' notes of the tetrachord. Similarly we have the triads , , , , , , . As some letters do not admit of this kind of differentiation, other methods are employed. Thus Δ is made to yield the forms (for ) Δ: from H (or B) are obtained the forms and : and from Z (or I]) the forms and . The modifications of N are / and : those of are and . The method of writing a Chromatic tetrachord is the same, except that the higher of the two moveable notes is marked by a bar or accent. Thus the tetrachord c c♯ d f is written . In the Diatonic genus we should have expected that the original characters would have been used for the tetrachords b c d e and e f g a; and that in other tetrachords the second note, being a semitone above the first, would have been represented by a reversed letter (gramma apestrammenon). In fact, however, the Diatonic Parhypatê and Tritê are written with the same character as the Enharmonic. That is to say, the tetrachord b c d e is not written , but : and d e ♭ f g is not , but . Let us now consider how this scheme of symbols is related to the Systems already described and the Keys in which those Systems may be set (tonoi eph' hôn tithemena ta systêmata melôdeitai). The fifteen characters, it has been noticed, form two diatonic octaves. It will appear on a little further examination that the scheme must have been constructed with a view to these two octaves. The successive notes are not expressed by the letters of the alphabet in their usual order (as is done in the case of the vocal notes). The highest note is represented by the first letter, A: and then the remaining fourteen notes are taken in pairs, each with its octave: and
- 39. each of thepairs of notes is represented by two successive letters— the two forms of lambda counting as one such pair of letters. Thus: On this plan the alphabetical order of the letters serves as a series of links connecting the highest and lowest notes of every one of the seven octaves that can be taken on the scale. It is evident that the scheme cannot have grown up by degrees, but is the work of an inventor who contrived it for the practical requirements of the music of his time. Two questions now arise, which it is impossible to separate. What is the scale or System for which the notation was originally devised? And how and when was the notation adapted to exhibit the several keys in which any such System might be set? The enquiry must start from the remarkable fact that the two octaves represented by the fifteen original letters are in the Hypo-lydian key— the key which down to the time of Aristoxenus was called the Hypo- dorian. Are we to suppose that the scheme was devised in the first instance for that key only? This assumption forms the basis of the ingenious and elaborate theory by which M. Gevaert explains the development of the notation (Musique de l'Antiquité, t. I. pp. 244 ff.). It is open to the obvious objection that the Hypo-lydian (or Hypo- dorian) cannot have been the oldest key. M. Gevaert meets this difficulty by supposing that the original scale was in the Dorian key, and that subsequently, from some cause the nature of which we cannot guess, a change of pitch took place by which the Dorian scale became a semitone higher. It is perhaps simpler to conjecture that
- 40. the original Dorianbecame split up, so to speak, into two keys by difference of local usage, and that the lower of the two came to be called Hypo-dorian, but kept the original notation. A more serious difficulty is raised by the high antiquity which M. Gevaert assigns to the Perfect System. He supposes that the inventor of the notation made use of an instrument (the magadis) which 'magadised' or repeated the notes an octave higher. But this would give us a repetition of the primitive octave e-e, rather than an enlargement by the addition of tetrachords at both ends. M. Gevaert regards the adaptation of the scheme to the other keys as the result of a gradual process of extension. Here we may distinguish between the recourse to the modified characters—which served essentially the same purpose as the 'sharps' and 'flats' in the signature of a modern key—and the additional notes obtained either by means of new characters ( and ), or by the use of accents ( , &c.). The Hypo-dorian and Hypo-phrygian, which employ the new characters and , are known to be comparatively recent. The Phrygian and Lydian, it is true, employ the accented notes; but they do so only in the highest tetrachord (Hyperbolaiôn), which may not have been originally used in these high keys. The modified characters doubtless belong to an earlier period. They are needed for the three oldest keys—Dorian, Phrygian, Lydian—and also for the Enharmonic and Chromatic genera. If they are not part of the original scheme, the musician who devised them may fairly be counted as the second inventor of the instrumental notation. In setting out the scales of the several keys it will be unnecessary to give more than the standing notes (phthongoi hestôtes), which are nearly all represented by original or unmodified letters—the moveable notes being represented by the modified forms described above. The following list includes the standing notes, viz. Proslambanomenos, Hypatê Hypatôn, Hypatê Mesôn, Mesê, Paramesê, Nêtê Diezeugmenôn and Nêtê Hyperbolaiôn in the seven oldest keys: the two lowest are marked as doubtful:—
- 41. It will beevident that this scheme of notation tallies fairly well with what we know of the compass of Greek instruments about the end of the fifth century, and also with the account which Aristoxenus gives of the keys in use up to his time. We need only refer to what has been said above on p. 17 and p. 37. It would be beyond the scope of this essay to discuss the date of the Greek musical notation. A few remarks, however, may be made, especially with reference to the high antiquity assigned to it by Westphal. The alphabet from which it was derived was certainly an archaic one. It contained several characters, in particular for digamma, for iota, and for lambda, which belong to the period before the introduction of the Ionian alphabet. Indeed if we were to judge from these letters alone we should be led to assign the instrumental notation (as Westphal does) to the time of Solon. The three-stroke iota ( ), in particular, does not occur in any alphabet later than the sixth century B.C. On the other hand, when we find that the notation implies the use of a musical System in advance of any scale recognised in Aristotle, or even in Aristoxenus, such a date becomes incredible. We can only suppose either (1) that the use of in the fifth century was confined to localities of which we have no complete
- 42. epigraphic record, or(2) that as a form of iota was still known—as archaic forms must have been—from the older public inscriptions, and was adopted by the inventor of the notation as being better suited to his purpose than . With regard to the place of origin of the notation the chief fact which we have to deal with is the use of the character for lambda, which is distinctive of the alphabet of Argos, along with the commoner form . Westphal indeed asserts that both these forms are found in the Argive alphabet. But the inscription (C. I. 1) which he quotes [27] for really contains only in a slightly different form. We cannot therefore say that the inventor of the notation derived it entirely from the alphabet of Argos, but only that he shows an acquaintance with that alphabet. This is confirmed by the fact that the form for iota is not found at Argos. Probably therefore the inventor drew upon more than one alphabet for his purpose, the Argive alphabet being one. The special fitness of the notation for the scales of the Enharmonic genus may be regarded as a further indication of its date. We shall see presently that that genus held a peculiar predominance in the earliest period of musical theory—that, namely, which was brought to an end by Aristoxenus. If the author of the notation—or the second author, inventor of the modified characters—was one of the musicians whose names have come down to us, it would be difficult to find a more probable one than that of Pronomus of Thebes. One of the most striking features of the notation, at the time when it was framed, must have been the adjustment of the keys. Even in the time of Aristoxenus, as we know from the passage so often quoted, that adjustment was not universal. But it is precisely what Pronomus of Thebes is said to have done for the music of the flute (supra, p. 38). The circumstance that the system was only used for instrumental music is at least in harmony with this conjecture. If it is thought that Thebes is too far from Argos, we may fall back upon the notice that Sacadas of Argos was the chief composer for the flute before the time of Pronomus, [28] and
- 43. doubtless Argos wasone of the first cities to share in the advance which Pronomus made in the technique of his art.
- 44. § 28. Tracesof the Species in the Notation. Before leaving this part of the subject it will be well to notice the attempt which Westphal makes to connect the species of the Octave with the form of the musical notation. The basis of the notation, as has been explained (p. 69), is formed by two Diatonic octaves, denoted by the letters of the alphabet from α to ν, as follows: η ι ε λ γ μ Ϝ θ κ δ λ β ν ζ α a b c d e f g a b c d e f g a In this scale, as has been pointed out (p. 71), the notes which are at the distance of an octave from each other are always expressed by two successive letters of the alphabet. Thus we find— β - γ is the octave e - e, the Dorian species. δ - ε " " c - c, the Lydian species. Ϝ - ζ " " g - g, the Hypo-phrygian species. η - θ " " a - a, the Hypo-dorian species. Westphal adopts the theory of Boeckh (as to which see p. 11) that the Hypo-phrygian and Hypo-dorian species answered to the ancient Ionian and Aeolian modes. On this assumption he argues that the order of the pairs of letters representing the species agrees with the order of the Modes in the historical development of Greek music. For the priority of Dorian, Ionian, and Aeolian he appeals to the authority of Heraclides Ponticus, quoted above (p. 9). The Lydian, he supposes, was interposed in the second place on account of its importance in education,—recognised, as we have seen, by Aristotle in the Politics
- 45. (viii. 7 adfin.). Hence he regards the notation as confirming his theory of the nature and history of the Modes. The weakness of this reasoning is manifold. Granting that the Hypo- dorian and Hypo-phrygian answer to the old Aeolian and Ionian respectively, we have to ask what is the nature of the priority which Heraclides Ponticus claims for his three modes, and what is the value of his testimony. What he says is, in substance, that these are the only kinds of music that are truly Hellenic, and worthy of the name of modes (harmoniai). It can hardly be thought that this is a criticism likely to have weighed with the inventor of the notation. But if it did, why did he give an equally prominent place to Lydian, one of the modes which Heraclides condemned? In fact, the introduction of Lydian goes far to show that the coincidence—such as it is—with the views of Heraclides is mere accident. Apart, however, from these difficulties, there are at least two considerations which seem fatal to Westphal's theory: 1. The notation, so far as the original two octaves are concerned, must have been devised and worked out at some one time. No part of these two octaves can have been completed before the rest. Hence the order in which the letters are taken for the several notes has no historical importance. 2. The notation does not represent only the species of a scale, that is to say, the relative pitch of the notes which compose it, but it represents also the absolute pitch of each note. Thus the octaves which are defined by the successive pairs of letters, β-γ, δ-ε, and the rest, are octaves of definite notes. If they were framed with a view to the ancient modes, as Westphal thinks, they must be the actual scales employed in these modes. If so, the modes followed each other, in respect of pitch, in an order exactly the reverse of the order observed in the keys. It need hardly be said that this is quite impossible.
- 46. § 29. Ptolemy'sScheme of Modes. The first writer who takes the Species of the Octave as the basis of the musical scales is the mathematician Claudius Ptolemaeus (fl. 140- 160 A.D.). In his Harmonics he virtually sets aside the scheme of keys elaborated by Aristoxenus and his school, and adopts in their place a system of scales answering in their main features to the mediaeval Tones or Modes. The object of difference of key, he says, is not that the music as a whole may be of a higher or lower pitch, but that a melody may be brought within a certain compass. For this purpose it is necessary to vary the succession of intervals (as a modern musician does by changing the signature of the clef). If, for example, we take the Perfect System (systêma ametabolon) in the key of a minor—which is its natural key,—and transpose it to the key of d minor, we do so, according to Ptolemy, not in order to raise the general pitch of our music by a Fourth, but because we wish to have a scale with b flat instead of b natural. The flattening of this note, however, means that the two octaves change their species. They are now of the species e-e. Thus, instead of transposing the Perfect System into different keys, we arrive more directly at the desired result by changing the species of its octaves. And as there are seven possible species of the Octave, we obtain seven different Systems or scales. From these assumptions it follows, as Ptolemy shows in some detail, that any greater number of keys is useless. If a key is an octave higher than another, it is superfluous because it gives us a mere repetition of the same intervals [29]. If we interpose a key between (e.g.) the Hypo-dorian and the Hypo- phrygian, it must give us over again either the Hypo-dorian or the Hypo-phrygian scale [30]. Thus the fifteen keys of the Aristoxeneans are reduced to seven, and these seven are not transpositions of a single scale, but are all of the same pitch. See the table at the end of the book.
- 47. With this schemeof Keys Ptolemy combined a new method of naming the individual notes. The old method, by which a note was named from its relative place in the Perfect System, must evidently have become inconvenient. The Lydian Mesê, for example, was two tones higher than the Dorian Mesê, because the Lydian scale as a whole was two tones higher than the Dorian. But when the two scales were reduced to the same compass, the old Lydian Mesê was no longer in the middle of the scale, and the name ceased to have a meaning. It is as though the term 'dominant' when applied to a Minor key were made to mean the dominant of the relative Major key. On Ptolemy's method the notes of each scale were named from their places in it. The old names were used, Proslambanomenos for the lowest, Hypatê Hypatôn for the next, and so on, but without regard to the intervals between the notes. Thus there were two methods of naming, that which had been in use hitherto, termed 'nomenclature according to value' (onomasia kata dynamin), and the new method of naming from the various scales, termed 'nomenclature according to position' (onomasia kata thesin). The former was in effect a retention of the Perfect System and the Keys: the latter put in their place a scheme of seven different standard Systems. In illustration of his theory Ptolemy gives tables showing in numbers the intervals of the octaves used in the different keys and genera. He shows two octaves in each key, viz. that from Hypatê Mesôn (kata thesin) to Nêtê Diezeugmenôn (called the octave apo nêtês), and that from Proslambanomenos to Mesê (the octave apo mesês). As he also gives the divisions of five different 'colours' or varieties of genus, the whole number of octaves is no less than seventy. Ptolemy does not exclude difference of pitch altogether. The whole instrument, he says, may be tuned higher or lower at pleasure [31]. Thus the pitch is treated by him as modern notation treats the tempo, viz. as something which is not absolutely given, but has to be supplied by the individual performer. Although the language of Ptolemy's exposition is studiously impersonal, it may be gathered that his reduction of the number of
- 48. keys from fifteento seven was an innovation proposed by himself [32]. If this is so, the rest of the scheme,—the elimination of the element of pitch, and the 'nomenclature by position,'—must also be due to him. Here, however, we find ourselves at issue with Westphal and those who agree with him on the main question of the Modes. According to Westphal the nomenclature by position is mentioned by Aristoxenus, and is implied in at least one important passage of the Aristotelian Problems. We have now to examine the evidence which he adduces to support his contention.
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