Plato's Perturbing Timaeus Scale as the Bait and Switch of Harmonic Mean (previously called Subcontrary Mean)

The "Timaeus" Scale

Jacques Handschin

Musica Disciplina

Vol. 4, Fasc. 1 (1950), pp. 3-42

Published by: American Institute of Musicology Verlag Corpusmusicae, GmbH

In the foot note we find this expose of the "bait and switch"





So Ottavio Tiby is emphasizing, just as Professor Richard McKirahan points out from Philolaus, that for Plato (from Achtyas), the fifths are "perturbing" because when reversed as fourths then can only be applied from within the octave as "octave division."

How does the author himself go into this detail - as he states he does not take "too concretely." In other words he just ignores this truth about the fourth in relation to the fifth... he performs the Bait and Switch!!





So the frequency of C as 2 and C' as 4 has 3 as G with the inverse of frequency as length so that the length is half of 4 as 2 as C but the geometric frequency is now the opposite octave being higher! And so the frequency of 3 as f requires the C and C' as octave to be switched around with the string length. This is obviously physically impossible and clearly the Bait and Switch out in the open. So he is literally stating that F=3=G at the SAME TIME. This is precisely the same paradox I have pointed out as noncommutative phase. He justifies it by stating that there is a different root tonic for the lengths as 6:4:3 and frequencies while claiming they have the same PITCH of "C" as the octave. Clearly the EAR hears a different root tonic of the "C" pitch - and so that is a LIE - it's the Liar of the Lyre exposed. 
The Bait and Switch relies on ignoring one of the three factors - in this case it is frequency, string length and pitch as geometric letter (C, F or G and C octave). 


So then when he refers to a colleague pointing out that the F as the Fourth can not be included - since it is not from within the octave - it's from a different octave and so it is Perturbing and he just says he relies on the ancient wisdom, not modern thought, so he just ignores that discrepancy...




The same intervals in reverse order as derived from the arithmetical (the Perfect fifth).

It is NOT more complicated if we just consider the components but it IS more complicated if we consider the whole.

So then instead of the harmonic mean as the Subcontrary mean of a different octave as a whole - we have to just look at the parts as harmonic partition.




So the reason the string lengths have to be rejected is because they are converted to geometric magnitude as the Bait and Switch!!

 

 So here is the Bait and Switch expressed quite clearly - the geometric mean must now be the "underlying" reality while the "strictly musical sense" must be rejected - in order to favor "our symmetrical tendency."

So to double check my claim I search Ottavio Tiby Perfect fourth Plato and this is what I get!!

Plato's Timaeus and the Missing Fourth Guest: Finding the Harmony of the Spheres (Studies in Platonism, Neoplatonism, and the Platonic Tradition)

by Donna M. Altimari Adler (Author)

In Plato's Timaeus and the Missing Fourth Guest, Donna M. Altimari Adler offers an original account of Plato's Timaeus from 35a-36d, yielding a new interpretation of the Timaeus scale and cosmic harmony imbedded in the text.

Publisher: BRILL (December 19, 2019)

Oh she doesn't mean the Perfect fourth - I forgot. I've seen that one before I think.

The Timaeus, the Decad, and the Harmonia: an Overview

In: Plato’s Timaeus and the Missing Fourth Guest

Author: Donna M. Altimari Adler


google review



Oh she is talking about the Perfect Fourth - has two chapters devoted to it - but not included in google preview............

Preface		xi
Acknowledgments		xxiii
List of Figures and Tables		xxvi
Introduction: Plato's Missing Fourth Guest		1	(15)
1 The Timaeus, the Decad, and the Harmonia: an Overview		16	(39)
2 Plato's Construction of the World Soul: the Text as a Number Generator from 35 A to a Conundrum in 36 B		55	(27)
1 Timaeus 35 A		60	(4)
2 End of Timaeus 35 A-Beginning of Timaeus 35 C		64	(7)
3 Timaeus 35 C and 36 A		71	(5)
4 Timaeus 36 A (con't) and 36 B		76	(6)
3 Solving the 36 B Conundrum: Deriving the Set of Sesquitertian Parts to Be Filled by Sesquioctave Intervals		82	(19)
1 Derivation of the Sesquitertian Parts		83	(18)
4 The Sesquioctave Operation within the Sesquitertian Parts		101	(23)
1 Deriving Matrix Numbers Not Generable from the 2:8/3 Interval		110	(3)
2 Special Mathematical Features of the Number Set Reflected in Table 24		113	(11)
5 The Musical Significance of Plato's Number Matrix: the Primary Timaeus Scale		124	(70)
1 Numerical Arrangement of the Timaeus Numbers with Key		125	(5)
2 The First Cognizable Fourth of Any Kind		130	(1)
3 The First Diatonic and Enharmonic Fourth		130	(3)
4 The "Model" Octave and the Perfect Disdiapason		133	(3)
5 Rise to the Perfect Disdiapason		136	(2)
6 First Octave of the Model Diatonic Octave Chain Containing Chromatic Elements		138	(1)
7 First Instances of Standard GPS, LPS, Diatonic UPS, and UPS in All Genera		139	(11)
7.1 Standard GPS		142	(1)
7.2 Standard LPS		142	(1)
7.3 Standard Diatonic UPS		143	(1)
7.4 Unacceptable Modulation		144	(1)
7.5 Standard Combined UPS in All Three Octave Genera		144	(6)
8 First Instances of Properly Timaean GPS, LPS, Diatonic UPS, and UPS in All Genera		150	(23)
8.1 The Timaeus GPS		150	(1)
8.2 The Timaeus LPS		151	(1)
8.3 Diatonic Timaeus UPS		152	(1)
8.4 Timaeus Combined UPS in All Genera		152	(21)
9 Possibilities for Modulation among Different Perfect Systems Arising within the Timaeus Numbers		173	(1)
10 The Primary Timaeus Scale		174	(5)
11 Some Other Modern Interpretations of the Timaeus Numbers and Timaeus Scale		179	(1)
12 The Feature of Ascending/Descending Ambiguity in Plato's Scale		180	(2)
13 Significance of the Chromatic Invasion for the Primary Timaeus Scale		182	(3)
13.1 Emergence of the Entire Unmodulating System in All Three Genera		182	(1)
13.2 Other Diatonic Possibilities Coincident with the Primary Timaeus Scale		183	(2)
14 The Orderliness of the Chromatic Invasion within the Primary Scale		185	(2)
15 Orderly Rise and Fall of Fifth Periodicity with the Decay of the Primary Scale		187	(3)
16 Grammar of Chromaticity in the Rise and Fall of Fifth Periodicity		190	(1)
17 Another Look at the Crantor Matrix		191	(1)
18 The Decad in the Rise, Wax, and Wane of the Primary Timaeus Scale		191	(3)
6 The Further Musical Significance of Plato's Number Matrix: the Many Secondary Timaeus Scales and Associated Musical Phenomena		194	(47)
1 The Many Secondary Diatonic Timaeus Scales Hidden in the Fabric		194	(17)
2 The Many Chromatic Timaeus Scales Hidden in the Fabric		211	(10)
3 The Many Enharmonic Timaeus Scales Hidden in the Fabric		221	(20)
3.1 Preliminary Observations		221	(3)
3.2 A Note on the Obvious		224	(3)
3.3 The Enharmonic Phenomena		227	(14)
7 The Musical Data of the Timaeus Vis-a-vis the Cutting of the Fabric, the Making of the "Chi," and the Cosmic Orbits		241	(31)
1 Division of the Material		242	(5)
2 Forming the x Figure		247	(10)
3 Bending the Arms to Form Circular Shapes		257	(4)
3.1 Volume		259	(1)
3.2 Surface Area		260	(1)
4 The Uniform Motion of the Whole without Variation		261	(1)
5 Separation of the Arms into an Outer and Inner Circle		262	(1)
6 Separation and Definition of the Motions of Same and Different		262	(2)
6.1 The Outer Band's Motion of the Same		262	(1)
6.2 The Inner Band's Motion of the Different		263	(1)
6.3 The Fitting Relationship of the Outer and Inner Bands		264	(1)
7 Elevation of the Motion of the Same to Primacy		264	(1)
8 Sixfold Split of the Inner Movement of the Different, i.e., the Octave Movement		264	(8)
8 Plato's Generalization of the Timaean Harmonia in Laws		272	(17)
Concluding Remarks		285	(4)
Appendices
Appendix 1 Verification of the Diesis Remaining after Insertion of Two Sesquioctave Intervals into a Sesquitertian Part for the Sample Sesquitertian Part 2:8/3		289	(16)
Appendix 2 The Archytan Alternative in the Pythagorean School		305	(3)
Appendix 3 Greater and Lesser Perfect Systems and Associated Questions		308	(12)
Appendix 4 Alternative Perfect Systems		320	(26)
Appendix 5 Two Overlapping Sequences of Doubles, Including Coincident Diatonic Octaves within Each, Bounded Entirely by Chromatic Factors of 1719926784		346	(39)
Appendix 6 Two Overlapping Sequences of Doubles, Including Coincident Diatonic Octaves within Each, Bounded Entirely by Chromatic Nonfactors of 1719926784		385	(22)
Appendix 7 Continuously Overlapping and Contiguous Chains of Doubles, Including Coincident Diatonic Octaves within Each, Bounded Entirely by Model Scale Numbers and Their Multiples		407	(24)
Appendix 8 Chromatic Scale Tables		431	(34)
Appendix 9 Specification of Trihemitones and Chromatic Scales in Which They Manifest		465	(31)
Appendix 10 Enharmonic Scale Tables		496	(58)
Glossary of Musical Terms and Concepts		554	(10)
Selected Bibliography		564	(6)
Subject Matter Index

https://www.kriso.ee/platos-%3Ci%3Etimaeus%3Ci%3E-missing-fourth-guest-finding-db-9789004389915.html


Donna M. Altimari Adler <donnaaltimari@comcast.net

Donna M. Altimari Adler <donnaaltimari@comcast.net>, “Plato’s Application of Philolaus’ Harmonic Law of Nature to the Generation of Plane Elements and Elemental Solid Bodies at Timaeus 53C-56C”


Number, Cosmogony, and Ontology in Plato, PresocraticThought, and Ancient Near Eastern and Greek Myth: Origins, Relations, and SignificanceDonna M. Altimari Adler <donnaaltimari@comcast.net>.This panel explores number as a feature or instrument of cosmogenesis, as a divider of being, as an index to the dynamism of being, or as an ontological index to patterns of being in ancient Near Eastern and Greek creation myths and theogonies; in Presocratic thought, as, for example, in Pythagoras and Philolaus; in Plato’s writings (including but not limited to the Parmenides, Republic, Timaeus, Laws), and in the later Platonic tradition (Plato as assimilated in Neoplatonic, Christian, Jewish, and Islamic thought), especially as it interpreted the Parmenides and Timaeus.It explores, inter alia, whether and how number was thought to mediate the descent of the Many from the One, in various accounts, and to bridge the gap between spiritual and material realities. Papers clarify the conceptions of number implied in the sources that they study, and help to elucidate the origins and foundations of the connection between number and cosmogony and number and ontology in Western tradition


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