I can see I can select a temperament from a list, or to create one myself.
However, I have a request - I need the octave to be "stretched".
That means, the octave is not 1200 cent. It should be about 20 cent bigger,
about 1,220 cents.
Can you permit input of a stretched octave, that is, allow input of twelve half-tones.
Now you allow only eleven, which means, I have no choice but a fixed octave size, 2/1.
Also, may I ask, do you just "assume" the samples in the SF2 sound bank as perfectly
in tune, since, if the samples are not exactly spaced, the numbers we enter are just deceiving.
What is your comment?
There is on internet a scientific paper which proved this idea as
irrefutably correct. To make good music, you must use a stretched octave.
I am now programming an additive synth with very accurate frequencies,
but it sounds horrible in classical music. Or do you have any suggestions?
What do you think about the accuracy of say, Philharmonik or Garritan?
My name is also on the "Scales List" where the over 1,000 scales are listed.
The gentleman who put me on the list was Mr John Chalmers, he published his
own research on the subject on the "tuning list":
source file: mills2.txt
Date: Mon, 9 Oct 1995 07:52:48 -0700
From: "John H. Chalmers" <firstname.lastname@example.org
Subject: Tuning & psychoacoustics - post 16 of 25
The evidence for a universal human preference for stretched intervals is
so overwhelming that it appears throughout the length and breadth
o`e psychoacoustic literature, both with Western and non-Western
"Dowland has reported that measurements of Western and non-Western fixed
pitch instruments suppprt Ward's conclusion that the perceptual octave is
some 15 cents larger than the physical or mathematical octave. Western
musical practice supports these conlusions (play sharp in higher octave).
Balinese gamelan tunings take advantage of this apparently widespready
characteristic of pitch perception to create a multi-octave beating ocmplex
in their fixed pitch instruments." [Erickson, Robert, "Timbre and the Tuning
of the Balinese Gamelan," Soundings, pg. 100, 1984]
Particularly revealing is "The 1215-Cent Octave: Convergence of Western and Non-Western
Data on Pitch Scaling," W. J. Dowling, Abstract QQ5, 84th meeting of the Acoustical Society of
America, Friday, December 1, 1972, p. 101 of program.
Yet more evidence for a universal preference for stretched octaves comes
from Sundberg, who found that the octave was as a rule played
significantly sharp by performing musicians, and was also preferred sharp
of the 2:1 in adjustment tests:
"Evidently the octave intervals in such stretched scales will exceed a 2:1
frequency ratio slightly. Thus, it is necessary to distinguish between the
*physical octave * (PO) which is defined as a 2:1 frequency ratio, and the
*subjective (musical) octave * (MO) that is perceived as pure. (...) As a rule,
the perceptual octave corresponds to a fundamental frequency ratio
exceeding 2:1." [Sundberg, J. and Lindqvist, J., "Musical Octaves and Pitch,"
JASA, 54(4), 1973, pp. 973-929]
Among the many implausible arguments which attempt to explain away this
mountain of experimental evidence for a preference for an octave interval
larger than the purportedly "pure" 2:1, most prevalent is the claim that
these "laboratory experiments do not represent real musical practice."
If this objection is correct, why does computer analysis of the frequencies
of pitches played during actual performances which show a uniform stretch
of the octave also show the same results as the laboratory psychoacoustic
experiments? And why do psychoacoustic measurements and experiments
stretching back over 150 years uniformly produce the same results?
"This disparity between the physical and subjective octaves is not a new
discovery. Stumpf and Meyer, using the method of constant stimuli, had 18
subjects judge pairs of successive tones as greater than, less than, or equal
to an octave. They lower tone was 300 cps and the upper tone was varied
around 600 cps. They found that 602 cps (the higher upper tone used)
received 52 percent "less," 43 precent "equal," and 5 percent "greater"
responses from the group, indicating that the mean subjective octave of 300
cps was somewhere above 602 cps (the present Fig. 4 gives about 605 cps).
Later von Maltzew, in an investigation on the identification of intervals in
the upper frequency range, found that a physical octave was more often
called a major seventh or below than a minor ninth or above. See C. Stumpf
and M. Meyer, Beit. Akust. Musikw., Vol. 2 ppg. 84-167, 1898. C. v. Malzew, Z.
Psychol. Vol. 64, pp. 16-257, 1913. [Ward., W.D., "Subjective Musical Pitch,"
Journ. Acoust. Soc. Am. , Vol. 26, No. 3, May 1954, pg. 374]
"The average standard deviation of repeated adjustments of sequential or
simultaneous octaves composed of sinusoids is on the order of 10 cents
(Ward, 1953, 1954; Terhardt, 1969; Sundberg & Lindquist, 1973). A range of
average deviations from 4 to 22 cents for adjustments of the other
intervals of the chromatic scale (simultaneous presentation) has been
reported by Moran and Pratt (1926). Rakowski (1976) reports variability--in
interquartile ranges--of 20 to 40 cents for both ascending and descending
melodic versions of the 12 chromatic intervals. Other general trends
evident from the results of adjustment experiments are...a tendency to
'compress' smaller intervals (adjust narrower than equal-tempered
intervals) and "stretch" wider intervals (adjust wider)." [Burns, E. M., and
Ward, W.D., "Intervals, Scales and Tuning," in The Psychology of Music, ed.
Diana Deutsch, 1982, pg. 250.]
"A number of measurements have been made of the intonation of musicians
playing variable-tuning instruments under actual performance conditions
(e.g., Greene, 1937; Nickerson, 1948; Mason, 1960; Shackford, 1961, 1962, a,
b). The results of these measurements have been summarized by Ward
(1970). They show a fairly large variability for the tuning of a given
interval in a given performance--ranged of up to 78 cents, interquartile
values of up to 38 cents. The mean values of interval tunings, in general,
show no consistent tendency to either just intonation or Pythagorean
intonation in either melodic or harmonic situations. The general tenedency
seems to be to contract the semitone and slightly expand all other intervals
relative to equal temperament. There is also some evidence of context-
dependent effecst (e.g., to play F# sharper than Gb (Shackford, 1962 a,b)].
Those results mirror, to a certain extent, the results of the adjustment and
identification experiments using isolated intervals (discussed in Sections
III A and III B) which showed a tendency to compress the scale for small
intervals and stretch the scale for large intervals, in both ascending and
descending modes of presentation.
"The above measurements were obtained for Western classical music, but
the same general tendencies are evident in intonation form a military band
(Stauffer, 1954), Swedish folk musicians (Fransson, Sundberg & Tjernland,
1970), and jazz daxophonists (Owes, 1974). Measurements of intonation
inperformance for Indian (Hindustani) classical music (jairazbhoy & Stone,
1963; Callow and Shepard, 1972) show similar variability." [Burns, E. M., and
Ward, W.D., "Intervals, Scales and Tuning," in The Psychology of Music, ed.,
Diana Deutsch, 1982, pg. 258.]
"Even the ubiquitous 5th itself is played, on the average, sharper than the
702 cents predicted; indeed, in Shackford's study, it is played sharpest in a
harmonic context, where the minimization-of-beat forces would be
expected to be the most active." (...) Thus evidence indicates strongly that in
musical performances the target pitch for frequencies actually produced in
response to a given notation is one that is just a shade sharper than that
called for by Et. In the 500 and 1000 Hz regions, even the subjective octave
(sacrosanct 2:1 in all theoretical systems) is about 1210 cents for pure
tones (Ward, 1954). In his studies, Shackford (1962 a,b) measured harmonic
10th, 11th and 12th and found that they were sharped to about the same
extent as 3rd, 4tha nd 5th.
"Boomsliter and Creel (1963) too have provided striking confirmation of this
theory. (...) ...it is clear from the sample dat they present aththe preferred
scale almost always is composed of tones consistently higher in frequency
than those of ET. For example, in three classical numbers (the Marseillaise,
a Bartok dance, and Mozart's Serenta Notturna), all notes above "do" are
preferred 4 to 23 cents sharp." [Ward, W.D., "Musical Perception," in
"Foundations of Modern Auditory Theory," ed. J.V. Tobias, Vol. 1, pp. 420-
The next post will examine data bearing on the third theory of hearing--
a model of the ear so far not dealt with as extensively as the other two.
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