Yahoo Tuning Groups Ultimate Backup tuning Articles available for summarization

I picked up a handful of articles from home and brought them to the
office today, with the idea of eventually summarizing and critiquing
them for the list. I'll list them here, and if anyone has a
particular interest in any of them, I'll start with those:

Barbour, James Murray. "Bach and the Art of Temperament", Musical
Quarterly vol. 33 no. 1, Nauray, 1947, pp. 64-89. Also in Garland
Library of HWM vol. 6, 1985, pp. 2-27.

Gann, Kyle. "The Outer Edge of Consciousness: Snapshots from the
Evolution of La Monte Young's Tuning Installations", in Sound and
Light: La Monte Young and Marian Zazeela, Bucknell Review vol. 15 no.
1, William Duckworth and Richard Fleming (eds.), Bucknell University
Press, Lewisburg, 1996, pp. 152-190.

Gerson, A. and J.L. Goldstein. "Evidence for a general template in
central optimal processing for pitch of complex tones", Journal of
the Acoustical Society of America vol. 63, 1978, pp. 498-510.

Goldsmith, David S. "An Electronically Generated Complex Microtonal
System of Horizontal and Vertical Tonality", Journal of the Audio
Engineering Society vol. 19 no. 10, Nov. 1971, pp. 851-858.

Hafner, Everett. "The Forty-Eight Revisited in Thirty-One", Well
Tempered Notes, November 1974, Motorola Scalatron Inc.

Johnston, Ben. "Tonality Regained", Proceedings of the American
Society of University Composers vol. 6, 1971, pp. 113-119.

Parncutt, Richard and Annabel J. Cohen. "Identification of microtonal
melodies: Effects of scale-step size, serial order, and training",
Perception & Psychophysics vol. 57 no. 6, 1995, pp. 835-846.

Terhardt, Ernst. "The Concept of Musical Consonance: A Link between
Music and Psychoacoustics", Music Perception vol. 1 no. 3, spring
1984, pp. 276-295.

Vermeulen, R. "Melodic Scales", Journal of the Acoustical Society of
America vol. 20 no. 4, July 1948, pp. 545-549.

Vos, Joos. "Purity ratings of tempered fifths and major thirds",
Music Perception vol. 3 no. 3, spring 1986, pp. 221-257.

Vos, Joos. "Subjective acceptability of various regular twelve-tone
tuning systems in two-part musical fragments", Journal of the
Acoustical Society of America vol. 83 no. 6, 1988, pp. 2383-2392.

Vos, Joos. "Spectral Effects in the perception of pure and tempered
intervals: Discrimination and beats", Perception & Psychophysics vol.
35, 1984, pp. 173-185.

Vos, Joos and Ben G. van Vianen. "Thresholds for discrimination
between pure and tempered intervals: the relevance of nearly
coinciding harmonics", Journal of the Acoustical Society of America
vol. 77, 1985, pp. 176-187.

🔗James <jmkh@uswest.net>

At 09:42 PM 8/1/01 +0000, Paul wrote:
>I picked up a handful of articles from home and brought them to the
>office today, with the idea of eventually summarizing and critiquing
>them for the list. I'll list them here, and if anyone has a
>particular interest in any of them, I'll start with those:

I would vote for the Vos papers. The topics implied in the titles are very relevant to my current interests.

Thanks,

>Barbour, James Murray. "Bach and the Art of Temperament", Musical
>Quarterly vol. 33 no. 1, Nauray, 1947, pp. 64-89. Also in Garland
>Library of HWM vol. 6, 1985, pp. 2-27.
>
>Gann, Kyle. "The Outer Edge of Consciousness: Snapshots from the
>Evolution of La Monte Young's Tuning Installations", in Sound and
>Light: La Monte Young and Marian Zazeela, Bucknell Review vol. 15 no.
>1, William Duckworth and Richard Fleming (eds.), Bucknell University
>Press, Lewisburg, 1996, pp. 152-190.
>
>Gerson, A. and J.L. Goldstein. "Evidence for a general template in
>central optimal processing for pitch of complex tones", Journal of
>the Acoustical Society of America vol. 63, 1978, pp. 498-510.
>
>Goldsmith, David S. "An Electronically Generated Complex Microtonal
>System of Horizontal and Vertical Tonality", Journal of the Audio
>Engineering Society vol. 19 no. 10, Nov. 1971, pp. 851-858.
>
>Hafner, Everett. "The Forty-Eight Revisited in Thirty-One", Well
>Tempered Notes, November 1974, Motorola Scalatron Inc.
>
>Johnston, Ben. "Tonality Regained", Proceedings of the American
>Society of University Composers vol. 6, 1971, pp. 113-119.
>
>Parncutt, Richard and Annabel J. Cohen. "Identification of microtonal
>melodies: Effects of scale-step size, serial order, and training",
>Perception & Psychophysics vol. 57 no. 6, 1995, pp. 835-846.
>
>Terhardt, Ernst. "The Concept of Musical Consonance: A Link between
>Music and Psychoacoustics", Music Perception vol. 1 no. 3, spring
>1984, pp. 276-295.
>
>Vermeulen, R. "Melodic Scales", Journal of the Acoustical Society of
>America vol. 20 no. 4, July 1948, pp. 545-549.
>
>Vos, Joos. "Purity ratings of tempered fifths and major thirds",
>Music Perception vol. 3 no. 3, spring 1986, pp. 221-257.
>
>Vos, Joos. "Subjective acceptability of various regular twelve-tone
>tuning systems in two-part musical fragments", Journal of the
>Acoustical Society of America vol. 83 no. 6, 1988, pp. 2383-2392.
>
>Vos, Joos. "Spectral Effects in the perception of pure and tempered
>intervals: Discrimination and beats", Perception & Psychophysics vol.
>35, 1984, pp. 173-185.
>
>Vos, Joos and Ben G. van Vianen. "Thresholds for discrimination
>between pure and tempered intervals: the relevance of nearly
>coinciding harmonics", Journal of the Acoustical Society of America
>vol. 77, 1985, pp. 176-187.
>
>
>
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🔗David Beardsley <davidbeardsley@biink.com>

🔗Paul Erlich <paul@stretch-music.com>

🔗jpehrson@rcn.com

🔗BVAL@IIL.INTEL.COM

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

Wow, what an offer.

All of them look interesting, but the following were
"higher order interesting looking" to use the scientific
term.

I'm probably more interested in the more 'musical' oriented,
like "48->31", Ben Johnston, and "Melodic Scales" (which
is at least titled very relevantly considering the recent
MOS thread with Jacky).

Bob Valentine

> Hafner, Everett. "The Forty-Eight Revisited in Thirty-One", Well
> Tempered Notes, November 1974, Motorola Scalatron Inc.
>
> Johnston, Ben. "Tonality Regained", Proceedings of the American
> Society of University Composers vol. 6, 1971, pp. 113-119.
>
> Parncutt, Richard and Annabel J. Cohen. "Identification of
> microtonal melodies: Effects of scale-step size, serial order,
> and training", Perception & Psychophysics vol. 57 no. 6,
> 1995, pp. 835-846.
>
> Terhardt, Ernst. "The Concept of Musical Consonance: A Link between
> Music and Psychoacoustics", Music Perception vol. 1 no. 3, spring
> 1984, pp. 276-295.
>
> Vermeulen, R. "Melodic Scales", Journal of the Acoustical
> Society of America vol. 20 no. 4, July 1948, pp. 545-549.
>
> Vos, Joos. "Purity ratings of tempered fifths and major thirds",
> Music Perception vol. 3 no. 3, spring 1986, pp. 221-257.
>
> Vos, Joos and Ben G. van Vianen. "Thresholds for discrimination
> between pure and tempered intervals: the relevance of nearly
> coinciding harmonics", Journal of the Acoustical Society of America
> vol. 77, 1985, pp. 176-187.

🔗James <jmkh@uswest.net>

At 02:12 AM 8/2/01 +0000, you wrote:
>--- In tuning@y..., James <
>jmkh@u...> wrote:
>
> >
> > I would vote for the Vos papers. The topics implied in the titles are > very
> > relevant to my current interests.
> >
>
>Which one in particular?

Well, I guess I would start with

> Vos, Joos. "Purity ratings of tempered fifths and major thirds",
> Music Perception vol. 3 no. 3, spring 1986, pp. 221-257.

I am going through a phase of being interested in how we perceive consonance and dissonance, and I gather that this paper would address that. It appears that his JASA paper would also, but I probably have access to that one locally.

Thanks again,

>
>You do not need web access to participate. You may subscribe through
>email. Send an empty email to one of these addresses:
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> tuning-normal@yahoogroups.com - change your subscription to individual > emails.
> tuning-help@yahoogroups.com - receive general help information.
>
>
>Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@y..., James <jmkh@u...> wrote:

> Well, I guess I would start with
>
> > Vos, Joos. "Purity ratings of tempered fifths and major thirds",
> > Music Perception vol. 3 no. 3, spring 1986, pp. 221-257.
>
> I am going through a phase of being interested in how we perceive
> consonance and dissonance, and I gather that this paper would
address
> that.

I think the Terhardt paper addresses that question more generally,
and this Vos paper focuses on a narrow component of it. Nevertheless,
I'll proceed. I'll put my own observations in square brackets.

Here's the abstract:

"In this study, the relationship between the degree of tempering of
musical intervals and the subjective purity was determined for fifths
and major thirds. The intervals were presented in isolation, that is,
they were not given in a musical context. For two simultaneous
complex tones the relationship between subjective purity and
tempering could be described by exponential functions. These
functions were obtained both for ratings on a 10-point equal-interval
scale and for subjective distances derived from preference data
collected by means of the method of paired comparisons. To verify to
what extent subjective purity had been determined by interference of
nearby harmonics, the spectral content of the tones was varied. For
both the fifths and the major thirds, interference of the various
pairs of nearly coinciding harmonics was canceled by deletion of the
even harmonics of the higher tone. This deletion resulted in higher
purity ratings, the effect being most prominent for the major third.
A further reduction of the potential interference between harmonics
was still more effective: for simultaneous sinusoidal tones,
subjective differences between pure and tempered intervals were much
smaller than for complex tones. Purity ratings for simultaneous
sinusoids presented at a low sound level were about equal to the
ratings for successive tones. The purity ratings were compared with
dissonance patterns predicted by models for tonal
consonance/dissonance. Only in a few conditions do the patterns
predicted by the model of Plomp and Levelt resemble the rating
patterns obtained, and the dissonance patterns predicted by the model
of Kameoka and Kuriyagawa are at variance with the purity ratings in
all conditions. Suggestions for revision of the models are given."

In the introduction, Vos cites his previous research about the
_discriminability_ between pure and tempered intervals. He found,
among other things, that (a) discrimination performance decreases
with increasing sum of p and q (where the pure ratio is p/q); (b)
that (not surprisingly) discriminability is poorer the smaller the
amount of tempering; and (c) that this difference is especially
pronounced for short tone durations (where, I'm guessing, the
intervals with small amounts of tempering fail to complete a full
beat and thus sound completely pure). This study, though, will not be
about discriminability, but about "subjective purity".

Vos begins by mentioning some previous studies that relate to the
evaluation of tuning systems. In

Rasch, R. A. "Description of regular twelve-tone musical tunings",
JASA Vol. 73 #3 (1983), pp. 1023-1035,

three measures were used to represent the concept of subjective
purity: quadratic mean tempering, linear mean tempering, and maximum
tempering. The measure of linear mean tempering implies that even a
very small amount of tempering will affect the subjective purity. The
measure of maximum tempering assumes that the worst interval in a
piece of music is the only factor that need be considered when
assessing its subjective purity. [Quadratic mean tempering, as a
measure of purity, represents a compromise between these sets of
assumptions.]

Hall, D. E. "The objective measurement of goodness-of-fit for tunings
and temperaments", _Journal of Music Theory_ vol. 17 (1973), pp. 274-
290,

this quadratic relationship between tempering and "undesirability" is
assumed, but he mentions two possible caveats to this approach. The
first is that some people find just intervals to be "insipid" while
finding slightly tempered intervals to possess greater "warmth". In

Roberts, L. A., & Mathews, M. V. "Intonation sensitivity for
traditional and nontraditional chords", JASA vol. 75 (1984), pp. 952-
959,

it was found that this effect is important for at least a subset of
the listeners studied. The second caveat is that for intervals
tempered by a large amount [more than about 27 cents, according to
the graph in Vos' article], where the beats are too rapid to be heard
individually, "undesirability" may no longer have any strong
relationship with the amount of tempering, and be roughly constant
instead. Vos concludes this section by noting that neither Hall nor
Rasch attempted to pursue the idea that the effect of tempering
depends on the _kind_ of musical interval, which would suggest using
unequal weights for the different intervals in the purity analysis of
tunings.

I'll continue next time with "The Rationale of the Experiments".

🔗Mats �ljare <oljare@hotmail.com>

🔗Paul Erlich <paul@stretch-music.com>

Next Vos discusses the complex effect of musical context on the
perception of roughness and intonation.

Shackford, C. "Some aspects of perception", _Journal of Music Theory_
vol. 5 pp. 162-202, vol. 6 pp. 66-90, 295-303

finds that the musical functions of the intervals, whether a piece is
tonal or atonal, and the specific ways in which diminished fifths and
augmented fourths are resolved, all seem to influence the intonation
behavior of string players. Vos claims [quite sensibly] that detailed
knowledge of the relationship between tempering and purity for
isolated intervals may faciliate [provide a basis of reference for?]
the interpretation of Shackford's results.

Vos' hypothesis for his experiments is that subjective purity of
isolated intervals depends both on the sensation of beats and
roughness, and on the perception of the actual size of the interval.
Specifically, Vos found in previous research that for temperings
larger than about 25 cents, the _direction_ of tempering could be
identified (wide or narrow), so he hypothesizes that for such
deviations, the subjective purity will be low _regardless_ of the
spectral content of the tones. Vos then discusses the details of the
rating system and statistical procedures.

Experiment 1: Tone 1 contained the first 20 harmonics with amplitude
proportional to 1/n. Tone 2 contained either the first 20 harmonics
or the first 10 odd harmonics. The phases of the harmonics were
chosen randomly [that prevents just intervals from ending up with
total constructive or destructive interference between coinciding
harmonics]. The relative levels of the two tones were such that the
amplitudes of the nearly coinciding harmonics were equal. 24
musically trained subjects participated. Four factors were varied
independently: (1) whether the interval was a fifth or a major third;
(2) the amount of tempering (0, ±2, ±4, ±6, ±8, ±10, ±15, ±20, ±25,
±35, and ±50 cents); (3) whether the higher tone had the first 20
harmonics or just the first 10 odd harmonics; (4) whether the tones
were 0.25 seconds or 0.5 seconds in duration. The central frequency
(geometric mean of the frequencies) was held near 370 Hz with small
random variations. The process of varying these factors in many
combinations, and repeating (to ensure reliability), meant a 4 hour
experimental session was needed.

Next time . . . the results of experiment 1 . . .

🔗Paul Erlich <paul@stretch-music.com>

🔗James <jmkh@uswest.net>

At 10:51 PM 8/2/01 +0000, you wrote:
>Next Vos discusses the complex effect of musical context on the
>perception of roughness and intonation.
>
>Shackford, C. "Some aspects of perception", _Journal of Music Theory_
>vol. 5 pp. 162-202, vol. 6 pp. 66-90, 295-303
>
>finds that the musical functions of the intervals, whether a piece is
>tonal or atonal, and the specific ways in which diminished fifths and
>augmented fourths are resolved, all seem to influence the intonation
>behavior of string players. Vos claims [quite sensibly] that detailed
>knowledge of the relationship between tempering and purity for
>isolated intervals may faciliate [provide a basis of reference for?]
>the interpretation of Shackford's results.
>
>Vos' hypothesis for his experiments is that subjective purity of
>isolated intervals depends both on the sensation of beats and
>roughness, and on the perception of the actual size of the interval.
>Specifically, Vos found in previous research that for temperings
>larger than about 25 cents, the _direction_ of tempering could be
>identified (wide or narrow), so he hypothesizes that for such
>deviations, the subjective purity will be low _regardless_ of the
>spectral content of the tones. Vos then discusses the details of the
>rating system and statistical procedures.
>
>Experiment 1: Tone 1 contained the first 20 harmonics with amplitude
>proportional to 1/n. Tone 2 contained either the first 20 harmonics
>or the first 10 odd harmonics. The phases of the harmonics were
>chosen randomly [that prevents just intervals from ending up with
>total constructive or destructive interference between coinciding
>harmonics]. The relative levels of the two tones were such that the
>amplitudes of the nearly coinciding harmonics were equal. 24
>musically trained subjects participated. Four factors were varied
>independently: (1) whether the interval was a fifth or a major third;
>(2) the amount of tempering (0, ±2, ±4, ±6, ±8, ±10, ±15, ±20, ±25,
>±35, and ±50 cents); (3) whether the higher tone had the first 20
>harmonics or just the first 10 odd harmonics; (4) whether the tones
>were 0.25 seconds or 0.5 seconds in duration. The central frequency
>(geometric mean of the frequencies) was held near 370 Hz with small
>random variations. The process of varying these factors in many
>combinations, and repeating (to ensure reliability), meant a 4 hour
>experimental session was needed.
>
>Next time . . . the results of experiment 1 . . .

I'm on the edge of my seat! Last time was probably at a Buck Rogers serial
in the forties.

>
>You do not need web access to participate. You may subscribe through
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> emails.
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🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@y..., James <jmkh@u...> wrote:

> I'm on the edge of my seat! Last time was probably at a Buck
Rogers serial
> in the forties.
>
> JB

All right . . . here are the results:

Vos found that in general, the relationship between the average
purity rating (y) and the amount of tempering (x) in cents can be
adequately described by means of the exponential function y = a*exp
(b*x). The values of a and b for each set of conditions are shown in
the following table:

Tone Musical Tempering Harmonics of Tone 2
Duration Interval Direction All Odd
-------------- --------------
a b r^2 a b r^2

0.5 Fifth Compress 8.8 .040 .99 9.7 .037 .97
Stretch 8.9 -.038 .99 9.4 -.035 .96
Major Third Compress 6.6 .028 .88 7.9 .023 .97
Stretch 7.0 -.026 .96 8.1 -.017 .98

0.25 Fifth Compress 8.6 .037 .99 9.2 .028 .99
Stretch 8.2 -.033 .98 8.8 -.028 .96
Major Third Compress 6.7 .025 .97 7.7 .022 .91
Stretch 6.7 -.019 .97 7.8 -.014 .93

Just to clarify, x is negative in the case of compression, and
positive in the case of stretching.

Any questions? Anyone want to graph these curves? I'll continue with
Vos's discussion of the results next time . . .