Volume 1 – Musical Elements

Volume 2 – Musical Signals

Errata for Second Printing

Errata for First Printing

Errata

Dr. Gareth Loy

Last Updated: 07/17/08

Rewards for Reporting Errata!

Musimathics Volume 1 Errata – Second Printing

Location

Problem

Correction

p. 174 Figure 6.14 caption text

Citation for Roederer is incorrect.

Text should read, “Adapted from Roederer 1973.”

Musimathics Volume 1 Errata – First Printing

Location

Problem

Correction

p. 14, last line

Sentence should read as corrected.

“Real numbers include all integers and all possible fractional and irrational values.”

p.22 Fig 2.10.b

Penultimate note in F major scale is E not E#.

Remove “#” after E.

p.29, Fig 2.19

The plus signs in the list “f + 2f + 3f + ...” are mathematically meaningless. Fig. 2.27 better represents partials.

A simple fix is to replace “+” with “,”, as shown to the right, representing the overtone frequencies as a series of integer multiples of a fundamental frequency. Alternately, to express the waveform that results from the combination of these sine components, let

p(x) = sin(2 pi x t)

where t is time, and then write p(f) + p(2f) + p(3f) + ....

p. 29 sec. 2.8.1

Change heading. (Not really an erratum, but it needs a better title.)

Heading reads: “Partials, Fundamentals, and Overtones”

Change to read “Fundamental, Partials, Harmonics, and Overtones”

p. 43, first sentence in section 3.3.2

Text refers to variable x in (3.1), but there is no such variable in that equation. Text should refer to variable k.

Text should read, “We can use equation (3.1) to add and subtract intervals. If k = 2 in that equation, then frequency f_k will be two octaves above frequency f_R. By the distributive law, we can rewrite this as...”

p.43, Fig. 3.1

Plus signs are mathematically wrong, similar to the error on p. 29, Fig 2.19.

The simplest fix is to remove the “+” signs. Alternately, the waveform can be expressed as a sum of sine components using the function p(x) as described above.

p. 45 top Figures 3.2, 3.3,

p. 49 at the bottom figure 3.5 at the  bottom

The ratio for C is given as 1/2.

The ratio for lowest pitch C should be 1/1, so that the octave above (2/1) would be correct.

p. 48 bottom, 7th sentence up from the bottom starting with "2.  The fifth is found by taking....."

Ratio is shown as 12:9

Ratio should be 9:6.

p. 104 Equation (4.12) and (4.13) Average Acceleration

Formulas (4.12) and (4.13) and their discussion are incorrect and misleading.

Please replace the entire section “4.10 Acceleration” with this PDF file.

p. 111

Section 4.14.1 presents a wrong and a misleading derivation of kinetic energy. Equation (4.28) is missing a factor of 1/2.

Please replace the entire section “4.14.1 Kinetic Energy” with this PDF file.

p. 111

Last line: “possess” is misspelled.

“posses” should be spelled “possess”.

p. 119, Equation (4.26)

Intensity of a sound does not increase with the square of the distance from a sound source but with its inverse. Corrected equation is shown at right.

p. 132 Equation (5.8)

Angular Acceleration Equation (5.8) is incorrect and misleading, similar to problem on p. 104.

Equation (5.8) should read as corrected.

p.134, bottom, in bold-italic text:

Improvement in wording to clarify concept.

Should read, “Circular motion is the result of a centripetal force applied at right angles to the instantaneous velocity.”

p. 143, sec. 5.5

2^nd para. 1^st sentence: remove ref. to E_k. Also, E_k=mv^2 is missing a factor of 1/2

Sentence and equation should read as corrected.

p.144

Equation (5.27) and the sentence enclosing it are missing a factor of 1/2.

Sentence and equation should read as corrected.

p. 174 Figure 6.14 caption text

Citation for Roederer is incorrect.

Text should read, “Adapted from Roederer 1973.”

p. 181 Table 6.1

Incorrect values for Bark #0 Lower Band Edge and Critical Bandwidth

Per [Zwicker 1961]: Bark 0 should be 0Hz for Lower Band Edge, 100Hz for Critical Bandwidth.

p.193 – 194, Section 6.13.5

Text incorrectly implies that if a speaker has intensity I, then at twice the distance the intensity is sqrt(I), whereas in fact it will be I/4. This mistake affects each equation on this page: sqrt should be replaced by a factor 1/4, and squaring by a factor of 4.

 Please replace the entire section “6.13.5 Distance Cues” with this PDF file.

p. 204 paragraph immediately below Eq. (7.5)

Text states “To determine the speed of sound we must determine the mass density of air...” However, I just gave the mass density of air in the previous sentence! What we really need is the average molecular mass of air.

“To determine the speed of sound, we must determine the average molecular mass of air...”

p. 210 sec. 7.8 2^nd para. 4^th sentence

Incorrect spelling.

“lightening” should be “lightning”

p. 226 Figure 7.24

The arrow labeled “Wavelength increases” should point up, not down.

p. 232 Equation 7.26

Formula for Doppler Shift in Two Dimensions is incorrect. The term u appearing inside the parentheses in the denominator should be outside the parentheses, as shown here.

I have created a Mathematica notebook that explains this equation better which is available here. A free player of Mathematica notebooks can be downloaded here. For a vector formulation of Doppler shift, see http://ccrma.stanford.edu/~jos/pasp/Doppler_Effect.html

p. 246 mid-page (5th paragraph)

Incorrect formula V = 7.5^ –4 m^3,

should be V = 7.5 x 10^ –4 m^3.

p. 257 Fig. 8.13

Figure subheadings are incorrect. Should read as corrected.

a) Fundamental (first harmonic)

b) Second harmonic

c) Third harmonic

p. 260 sentence before run-in heading “Bar with Free Ends”

Sentence reads, “Plugging these values into (8.18) for n = 1,2,3,4,5 yields a fundamental and partials shown in the last column of table 8.3.”

Sentence should read, “Plugging these values into (8.18) yields a fundamental and partials shown in the last column of table 8.3.”

Delete “for n = 1,2,3,4,5”

p. 359 Third sentence into section 9.17.5

It would be better to say that Voss & Clark used a Gaussian noise generator than a uniform noise generator.

Text reads:

“To test this hypothesis, they synthesized melodies of three types using a computer: the first type made tone and rhythmic selections with a uniform...”

But should read:

“To test this hypothesis, they synthesized melodies of three types using a computer: the first type made tone and rhythmic selections with a Gaussian...”

p. 396

Description of the Fusion Petri net structure is misleading. The text reads, “Only one of the two input places can trigger M1,” however this does not agree with the structure of the diagram to the right of that paragraph, nor with the definition of the Petri net firing rule given on page 391.

The text should read as corrected.

Both of the two input places are needed to trigger M1.

p. 460, notes for Chapter 5, note 4.

Text states incorrectly that circular motion is the vector sum of centripetal force and linear velocity.

Text should read as corrected.

Circular motion is the result of a centripetal force applied at right angles to the instantaneous velocity.

Musimathics Volume 2 Errata

Location

Problem

Correction

p. 65 Eq. (2.31)

The last term in the expression reads: \frac{7^{7}}{7!}

but should read: \frac{z^{7}}{7!}

Please substitute the equation to the right.

p. 79, Eq. (2.53)

Shows the sum of the two phasors on the left side of the equation, but should show the difference.

p. 83, Section 2.6.12

Text reads, “sin x = –sin x, “ which is not true.

What is true is that sin –x = –sin x.

p. 84, Figure 2.25 and Table 2.3

Text continues to assert that for odd functions, f(x) = –f(x), but again, this is incorrect.

The correct definition of an odd function is one in which f(–x) = –f(x).

p. 135 Matrix figure in Section 3.4.1

Top and bottom rows are correct. Middle rows show the superscript k+1 in the second column instead of k. Please substitute the corrected matrix figure to the right.

p. 164 (4.8) and p 165 (4.9) the convolution sequence is incorrect. Row 1 is OK but rows 2 through 5 should have a leading zero and delete the trailing zero.

The summation line has 5+5 elements and should only have 5+5-1 elements. Delete the trailing zero.

p. 171 Figure 4.13 some values of sampled functions f(n) and g(n) and their product function are incorrect. The graphical functions in this figure are correct, including the spectral plot.

There are really two problems here. First, there are transcription errors in the sampled functions f(n) and g(n). More fundamentally, however, the figure implies that the graphical functions can be reproduced from the sampled functions, which is not true, given how highly truncated the sample values are. Basically, this figure and accompanying text do not provide enough information to adequately demonstrate what is being discussed.

The reader interested in a fuller understanding of the steps shown in this figure and corrected sampled functions are referred to this PDF file. If you prefer, here is the Mathematica notebook. A free Mathematica player for this notebook is available for download here.

p. 183 first sentence of Section 4.3

This is not technically an errata, but some readers have tripped over this point, so I'm going the extra mile to explain it. Replace the first sentence of this section with the following:

Given that the length of two convolved functions f and g is N_f + N_g - 1, and recalling that we’ve defined as zero any values that lie outside that range, we will get the same result if we set the limit of summation in equation (4.1) to N_f + N_g - 1 or to any larger value, even to infinity. (The “only” difference is all those extra zero terms in the output function h but the numerical result is not affected.) The benefit is that we can now relate convolution directly to the discrete Fourier transform which likewise has an infinite limit of summation.

p. 215 unnumbered display equation just after Equation (5.31)

The term - pi T, should be -pi over 4 T.

p. 215 Figure 5.14

The Radians vertical axis should read from top to bottom 0, -pi over 4, -pi over 2.

P 216 Equation (5.32) Real Frequency Response

The coefficient t should be T.

p. 229 Text following Equations (5.52) and (5.53)

The range of n is misstated as n = 0, 1, 2, ... in text following these equations.

Should read in both places n = 1, 2, 3, ...

p. 231 last paragraph first sentence

Incorrect definition of z. The exponent of e should be positive. The sentence reads:

“Now consider what happens when we take equation (5.70), which represents the factored form of H, and set e^—iwT...”

It should read:

“Now consider what happens when we take equation (5.70), which represents the factored form of H, and set e^iwT...”

p. 227 Figure 5.18 b.

Figure 5.18 b should show a spiral shrinking counterclockwise.

p. 227 Figure 5.18 c.

Figure 5.18 c should show a spiral expanding counterclockwise.

p. 227 table just before section 5.11.2.

|z^n| < 1 Description is incorrect, should be clockwise.

|z^n| > 1 Description is incorrect, should be clockwise.

|z^n| < 1 Contracting clockwise circle

|z^n| > 1 Expanding clockwise circle

p. 239 paragraph above equation (5.72)

Incorrect assertion about e to imaginary powers. Text reads:

and |e^anything| = 1

Text should read:

and |e^{i anything}| = 1

p. 246 text above equation (5.82)

Incorrect definition. Text reads:

we know we can say H(e^—iw) = a₀ + a₁ e^—iw

Text should read:

we know we can say H(e^iw) = a₀ + a₁ e^—iw

p. 374

Mid-page, for k = 0 the table incorrectly gives frequency as DC. Correct frequency for k = 0 is 1.

Text should read (only first 4 columns shown here):

p. 375

Bottom of the page, for k = 0 the table incorrectly gives frequency as DC. Correct frequency for k = 0 is 1.

Text should read (only first 4 columns shown here):

p. 521 unlabeled display equation immediately before Equation (A.20)

Parentheses are missing after the coefficient i.

Errata Rewards for Musimathics

I have adopted Donald Knuth's reward system to encourage readers to report errors in Musimathics. The first finder of any error receives $2.56 (one hexadollar). Significant suggestions are also worth $0.32 each.
Knuth notes that, "If you are really a careful reader, you may be able to recoup more than the cost of the books this way."

Please send your comments by email to Errata << at >> Musimathics.com.

You can also communicate with me by snail mail:

    Gareth Loy
    POB 151185
    San Rafael, CA 94915.

I will attempt to reply to all such messages within six weeks of receipt.

Please do not send email to the above address except to report errors in Musimathics.  If you report an error via email, please do not include attachments of any kind, and use plain ASCII  text.  For representing mathematical equations in plain text, I suggest http://mathforum.org/dr.math/faq/faq.typing.math.html or http://www.karlscalculus.org/email.html.  The character set should be Western.

I'm very sorry, but I am not sufficiently fluent in any language besides English to discuss anything more complicated than travel directions. Though I can usually make out French and Spanish if I work at it, it will probably be best for all concerned if you communicate with me in English.

Regards,
Gareth Loy