Ratio scales of sugar sweetness
HOWARD R. MOSKOWITZ2 BAR VARD UNIVERSITY
In a series of 10 experiments, groups of intensities. The sensory ratio is not directly experiments on the growth of sensory Os judged the sweetness of 16 sugars. The measured, although it could be measured intensity suggest that, for more than two results suggest that, for all sugars except by asking Os to estimate the relative dozen perceptual continua, a power mannose, the intensity of sweetness grows magnitude of sweetness of sugars at the function, S =kln, relates sensory intensity, asa power function ofconcentration, with same concentration. This estimation S, to physical intensity, I. In log-log an exponent of about 1.3. The relative procedure has proved effective in coordinates, the power function becomes a sweetness of sugars was determined using measuring sensory ratios. line, log S = n log I + log k, with slope n both molarity and per cent by weight. With The present study concerns the function and intercept k. Much attention has been both measures, sucrose and fructose were relating sweetness to concentration of directed to the exponent (slope n) of each the sweetest sugars. The order of the sugar and is designed to compare the continuum because it is a relatively remaining sugarsin the sweetness hierarchy parameters of the function across different invariant parameter across different was partly a function of the measure of sugars. The sensory judgments of sweetness experiments. The exponent characterizes concentration. The variability of the were obtained by magnitude estimation, a the transformation of stimulus ratios into magnitude estimates of sweetness was method in which Os assign numbers to sensory ratios and is independent of the roughly proportional to the stimulus stimuli in proportion to the perceived absolute physical intensities of the stimulus concentration, supporting Weber's law. sweetness. The results of many similar and of the modulus of the scale chosen by Table 1 The sweetness of sugars can be scaled Stimulus Concentrations along two major dimensions: quality and Sugar Family Sugar 2 3 4 5 6 intensity. Little work appears to have been done to quantify the differences in quality Triose Glycerol *2.00 4.00 8.00 16.00 32.00 64.00 M.W.92.09 0.22 0.44 0.88 1.80 3.12 8.01 among sugars, other than a listing of the C3H803 more obvious sensory effects. For example, Pentose Arabinose *2.00 4.00 8.00 16.00 the sweetness of glucose differs markedly M.W.150.13 0.13 0.27 0.54 1.13 from that of sucrose, with a burning side C5Hl()05 Xylose *2.00 4.00 8.00 12.00 32.00 taste often appearing at high 0.13 0.27 0.54 0.83 2.40 concentrations (Amerine, Pangborn, & Aldohexose Glucose *2.00 4.00 8.00 16.00 32.00 50.00 Roe s sIe r , I 965) . Man nose, a M.W.180.16 0.11 0.22 0.46 0.94 2.02 3.40 monosaccharide similar in structure to C6H1206 Galactose *2.00 4.00 8.00 16.00 32.00 glucose, tastes both bitter and sweet 0.11 0.22 0.46 0.94 2.02 (pangborn & Chrisp, 1966; Pangborn & Mannose *2.00 4.00 8.00 16.00 32.00 Gee, 1961). 0.11 0.22 0.46 0.94 2.02 Differences in sweetness intensity have been much explored. Sugars differ in their Ketohexose Fructose *2.00 4.00 8.00 16.00 32.00 50.00 sweetening power, forming a hierarchy, M.W.180.16 0.11 0.22 0.46 0.94 2.02 3.40 with sucrose and fructose at the apex and C6H1206 Sorbose *2.00 4.00 8.00 16.00 32.00 lactose and raffinose at the base (Cameron, 0.11 0.22 0.46 0.94 2.02 1947). Complications in the hierarchy Sugar alcohol Sorbitol *2.00 4.00 8.00 16.00 32.00 50.00 often arise because of the presence of M.W.182.16 0.11 0.22 0.45 0.91 1.89 3.09 anomers having similar chemical properties C6H1406 Mannitol *2.00 4.00 8.00 16.00 but differing from each other primarily in 0.11 0.22 0.45 0.91 their ability to rotate light. The gustatory Dulcitol *2.00 4.00 response is different to each anomer, so 0.11 0.22 that at equal concentrations, the two forms differ in sweetness, e.g., a glucose is Methylhexose Rhamnose *2.00 4.00 8.00 16.00 32.00 sweeter than {3 glucose, whereas {3 lactose is M.W.164.16 0.12 0.25 0.50 1.03 2.17 sweeter than its anomer, a lactose C6H1205 Disaccharide Sucrose *2.00 4.00 8.00 16.00 32.00 64.00 (pangborn & Chrisp, 1966; Pangborn & M.W.342.30 0.06 0.12 0.24 0.50 1.06 2.45 Gee, 1961). H22011 C12 Maltose *2.00 4.00 8.00 16.00 32.00 50.00 Traditionally, relative sweetness has 0.06 0.12 0.24 0.50 1.06 1.77 been defined as the ratio ofconcentrations Lactose *2.00 4.00 8.00 16.00 of substances matching in sweetness. For 0.06 0.12 0.24 0.50 example, if 8% maltose and 4% glucose taste as sweet as 2% sucrose, then maltose Trisaccharide Raffinose *2.00 4.00 8.00 16.00 is 25% as sweet as sucrose, whereas glucose M.W.594.52 0.03 0.07 0.14 0.28 is 50% as sweet. The tacit assumption made C18H32016SH20 is that the ratio of physical concentrations .. Asterisks indicate that concentration is expressed as per cent by weight; non-asterisked rows that match defines a like ratio of sensory indicate that concentration is expressed as molarity.
Perception & Psychophysics, 1970, Vol. 7 (5) Copyright 1970, Psychonomic Journals, Inc., Austin, Texas 315 Table 2 and Cambridge tap water. Sucrose was Conditions of Experiment obtained from a commercial brand ofcane No. Judgments sugar (Domino). Solutions were stored at Experi- of per SoC and were sampled at room ment Observers Observer Stimuli temperature (19°C). Prior to use, solutions 40 Fructose, Galactose, Glucose, Lactose, Maltose, Mannitol, remained under refrigeration for 3 days in Sorbitol, Sucrose order to ensure mutarotation to an 2 10 2 Maltose, Mannose, Raffinose, Sorbose, Sucrose equilibrium mixture of anomers. 3 10 2 Arabinose, Mannose, Raffinose, Rhamnose, 'Sucrose During the experimental session, the stimulus solutions were presented to the 0 4 10 2 Dulcitol, Galactose, Mannitol, Sorbitol, Sucrose in paper cups, with S to 10 ml of solution 5 10 2 Lactose, Raffinose, Sorbose, Sucrose, Xylose in each. The solutions were given in an 6 10 2 Fructose, Glucose, Glycerol, Sucrose irregular order to the 0, who first sampled 7 20 2 Sucrose, Na Cyclamate*, Ca Cyclamate", Na Saccharin* the solution, then gave a magnitude 8 20 2 Sucrose, Artificial Sweetening Compounds* estimate of sweetness, and finally rinsed 9 30 1 Glycerol, Sucrose, Artificial Sweetening Compounds* with tap water. There were no restrictions 10 30 1 Sucrose, Na Saccharin", Sucrose and Na Saccharin under on time, so that the 0 completed the different levels of solution viscosity* session as quickly as he wished (usually in • Results not reported here 20 min). He was given the following written instructions: the O. The intercept k is the scale factor different compounds at one point on the "In front of you is a series of paper cups and may change from experiment to concentration continuum. At the filled with stimulus solutions. Your task is experiment without affecting the exponent concentration given by the intercept, the to tell how sweet they seem by assigning (Stevens, 1960). sweetness of different sugars may be easily numbers proportional to sweetness. If the The exponent for sugar sweetness compared. Meaningful intercept may be second stimulus is nineteen times as sweet appears to be about 1.3. Stevens reported ensured by presenting different sugars as the first, assign it a number nineteen an exponent of 1.3 for both sucrose and during the same experimental session, times as large. If it seems one-eleventh as glucose, and that value for sucrose was thereby allowing the 0 to scale them sweet, assign it a number one-eleventh as confirmed by magnitude estimation and relative to a common unit. That was done large, and so forth. Use numbers, fractions, cross-modal matching (with loudness) by in the present study by using a core set of and decimals, but make each assignment Moskowitz (1968). On the other hand, six sucrose concentrations in every proportional to the sweetness as you Gregson and Russell (1965) reported an experiment. perceive it." exponent of about 0.6 for the sweetness of sucrose. A discussion of their results and of STIMULI AND PROCEDURE ANALYSIS OF THE MAGNITUDE others' appears in Moskowitz (1968). In 10 experiments, different groups of ESTIMATES When the relative sensory intensities of Os from a pool of 83 judged the sweetness Since magnitude estimates are usually different sugars are of interest, the of 16 sugars (Tables I and 2) by magnitude distributed log-normally (J. C. Stevens, intercept also becomes important, since it estimation. All solutions except sucrose 1957), the geometric mean is usually a gives the relative sensory intensity of were made from reagent-grade chemicals proper measure of central tendency. In the present study, however, it was often inapplicable, since many Os gave magnitude estimates of "0" when they BEFORE NORMALIZATION AFTER NORMALIZATION 100 ~ J could not detect sweetness. In this on situation, the median is the preferred on • measured. For computer analysis, how '"z 50 ... •Q) ever, judgments of "0" were replaced ~ l' '" vJa. by a number equal to 0.1 times the lowest on• .. .. ! 20 • 't- magnitude estimate given by the O. The on • '"0 medians and the geometric means of the a: •
316 Perception & Psychophysics, 1970, Vol. 7 (5) Table 3 Parameters of the Power Functions for Sugars (S = kCn). The parameters were obtained for two cases: the exponent was fixed at 1.3, or the exponent was not fixed, Molarity Per Cent by Weight n = 1.3 Least-Squares Fit n = 1.3 Least-Squares Fit Rank k R.S.* n k R.S.* Rank k R.S.* n k R.S.* Sucrose** 1 50.0 1.00 1.33 46.4 1.00 1 0.54 1.00 1.35 0.43 1.00 Fructose** 2 20.4 0.41 1.33 21.2 0.46 2 0.49 0.91 1.38 0.43 1.00 Raffinose 3 16.6 0.33 0.63 3.5 0.07 15 0.08 0.15 0.64 0.27 0.63 Maltose 4 15.0 0.30 1.20 13.4 0.28 12 0.17 0.31 1.25 0.19 0.44 Lactose 5 11.0 0.22 0.89 5.5 0.12 14 0.12 0.22 0.98 0.23 0.53 Dulcitol 6 10.8 0.22 0.24 1.5 0.03 5 0.25 0.46 0.24 0.74 1.72 Glucose 7 9.4 0.19 1.18 8.9 0.19 4 0.24 0.45 1.26 0.22 0.50 Galactose 8 9.2 0.18 1.36 9.6 0.21 6 0.23 0.42 1.43 0.17 0.40 Sorbose 9 9.1 0.18 1.12 7.9 0.17 7 0.22 0.41 1.17 0.19 0.44 Sorbitol 10 8.4 0.17 1.22 8.1 0.17 9 0.20 0.37 1.17 0.29 0.68 Mannitol 11 7.7 0.15 1.24 7.7 0.16 11 0.18 0.33 1.27 0.19 0.44 Arabinose 12 6.9 0.14 1.16 6.0 0.13 8 0.21 0.39 1.20 0.25 0.58 Rhamnose 13 6.7 0.14 1.29 6.8 0.15 10 0.19 0.35 1.34 0.17 0.40 Glycerol 14 5.2 0.10 1.09 4.7 0.10 3 0.27 0.50 1.13 0.40 0.93 Xylose** 15 4.8 0.10 1.32 4.9 0.11 13 0.14 0.26 1.37 0.19 0.44
* R.S. = Relative sweetness (sucrose = 1.0). Relative sweetness was determined by the ratio of magnitude estimates at the concentration given by the intercept. ** Functions for sucrose and fructose were obtained by considering only the lowest four concentrations of each (2%. 4%. 8%. 16%). The xylose function was analyzed without considering the median magnitude estimate given to 2% xylose.
~ I OFRUCTOSE-EXP. I .-ExP. 6 o GALACTOSE - EXP. I • - EXP. .. 100 o SORBOSE - UP. 2 • - EXP, 4 6,MANNOSE - ExP. 2 .. - EXP. :3 100 C ARASINQSE HExOSES OGI.UCOSE -[XP. I .- [xP. 6 • RHAMNOSE - E XP. 3 o x'l'LOSE ~ PENTOSES ~ .0 ...z ~ ... '0 ~ / 10 ~
... ~ s- ~ ~ c ~ / ~ ~ ~ , o E c 'f ~ ~ I i Z •• ~ ~ ~ • 0)1 {'::, {'::, ~ ~ "[ z z ~ ~ ., I Q f;: ~ ...l-_~_ ~. ~ i { ~_.-L~ _~• ...... l. I ...... • . __ ._...... ---L-- __ .1.- L-_----L....---L_---L-.-- . (",_ --'------/ .1 .--.J..-.._ ... ~ .~ 1.0 Z.O .J .2 .5 1.0 2.0 ~~.,c----o~~---.2 ~"c-"",''=.o--::'::-'''''''',-JI .1 •1 .1 .2 .1 .2 .1 .2 .5 .. .L,: .s 5~O ., .e ., .. MOLARITV OF SUGAR MOLARIT Y OF SUGAR A a r-..... , I ., I I ,. I
I I o MALTOSE - Ell!! I • - EXP.2 o LACTOSE - EXP. r • - EXP.S ~ ~~:~l~~~ OLIGOSACCHARIDE 5 g =:::.: SUGAR ALCOHOLS (POLyGLYCOLSI /":., FtAFFlNOSE-EXp'2 8-EllR3 &-EXP.5 100 0 DULCITOL 'r o GLYCEROL - ExPo 6 •- El(P.9 so i o ~ ~ 20 o 20 • ~ 10 10 r :. ~ . s ~ o 0 ~ • ~ .5 z ~ o ~ .2 .2 ~ I 1 , ., .s ., .s ., .s ., .01 .02 .os .01 .02 MOLARI TY OF SUGAR c D
Fig. 2. Median magnitude estimates of the sweetness of (A) pentoses, (B) hexoses, (C) sugar alcohols (polyglycols), and (D) oligo saccharides (heavier sugars) after normalization.
Perception & Psychophysics, 1970, Vol. 7 (5) 317 provided a least-squares fit of the exponent suggesting differences in the Os' measure of concentration and always gives and intercept of the simple power perceptions at low concentrations. In one a slightly steeper slope (Moskowitz, 1968). function, S =kIn, to the magnitude experiment, the sweetness of dilute estimates. In addition, Psychofit provided mannose solutions decreased with summary statistics on the responses, increasing concentration, whereas in the Sweetness Functions from Other Studies including the variability of the judgments other, it increased in the expected manner. The foregoing premise, that sweetness before and after the scale units used by The confusion of the sweet taste and the conforms to a power function of different Os had been equalized by bitter side taste reported to accompany concentration, is supported by other data modulus equalization (Lane, Catania, & mannose may be implicated in this obtained by one or another matching Stevens, 1961). anomalous result. method (Fig. 3). Matching functions with a Since the absolute levels of the median Sweetness functions may be related to slope of 1.0 (in log-logcoordinates) suggest judgments differed in each experiment, a two measures of concentration, one using that both sugars have equal (but normalization procedure was used to bring molarity and emphasizing the number of undetermined) exponents in the power the magnitude estimates into agreement molecules in solution and the other using law, whereas functions with slopes less with each other. The geometric means of per cent by weight (grams solute per 100 g than 1.0 indicate that the abscissasugar has the magnitude estimates given for 4%, 8%, solution) and emphasizing the weight of the lower exponent, i.e., grows less rapidly 16%, and 32% sucrose (Table 1) were solute in solution. The slopes and in sweetness. Glucose sweetness probably multiplied by a number that made their intercepts differ, depending upon the grows slightly more rapidly than sucrose grand mean come to 10.0. The geometric measure of concentration (Table 3). Per sweetness (Functions 1·3, Fig.3A), means and medians for the other sugars cent by weight constricts the range of the whereas the sweet taste of sucrose, lactose, scaled in the same experiment were also normalized by the same multiplier. A ;:: 1 "' .--,--.---,----,r-----,--,.--,-----,--,----, different multiplier was needed in each ~ 100 6 - PANGBORN, 1963 experiment. The normalization suppressed i •- NIEMAN,I958 2 some of the intercept variability and ~ 50 o - LICHTENSTEIN. 1948 allowed the slope of the sucrose function :.. (Fig. I) to emerge more clearly. ~ 20 u II: ~ RESULTS ...lL 10 Form of the Sweetness Function o "5 For 15 sugars (Figs. I and 2 and U Table 3), the median magnitude estimate .,.'"..J of sweetness grew as a power function of l!; 2 concentration. Lines drawn through the z medians have slopes of 1.3, a value chosen ~ ~ on the basis of previous estimates of the II: sweetness exponent (Moskowitz, 1968; E Stevens, 1969). Although exceptions ~ occur, a single representative exponent u .2 appears to be justified. For each sugar ~ (except mannose), a least-squares fit was ~ .1 .2 .5 1.0 2.0 5.0 .1 .2 .5 1.0 2.0 5.0 10.0 20.0 50.0 also obtained for the slope and intercept. !q PERCENT SUCROSE BY WEIGHT The results (Table 3) suggest that, in most ~ .. cases, the exponent departs only slightly from 1.3. I I Several stimulus concentrations were not o NIEMAN,I958 included in the foregoing analysis. .... 6 PANGBORN. 1963 - FRUCTOSE Magnitude estimates given to 2% xylose r 50 ~ 6 PANGBORN.1963 - LA CTOSE 4 6 (0.13 M) depart from the rest of the xylose ... ~ function and should not be blindly ,:,. 20 included in analyses by least squares. On III I the other hand, reproducible curvature at ~ 10 the top of the sucrose and fructose ...u functions (Figs. I and 28) suggest that ...II: 5 lL systematic departures from the power z function are occurring, so that these higher ~ 2 .... concentrations call for separate .. II: consideration. .... FRUCTOSE ...Z Mannose (Fig. 28) is the only sugar of U z .5 o the 16 that did not grow as a power u function of concentration. The median .,. z .2 magnitude estimates were erratic, r u !q .1 L------.l-----:e----~H-.i--~-_+-~___,:_'_::_-__='::__+:____::c!_::.----l Fig. 3. Equal-sweetness functions traced :Ii out by matches between sucrose, glucose, fructose, and lactose.
318 Perception & Psychophysics, 1970, Vol. 7 (5) MOLARITY o MALTOSE o l,.ACTOSE 1.0 OLiGOSACCHARIDES • • PRESENT [)(PERIME.,r 10 6 RAFFINOSE .. a PAUL. 1921 o SUCROSE .. . • OEuTSCH- R£NN[R.1937 o .. . a CAMERON,I947 o Z .7 I- • lAWRENCE AND FERGUSON. ISS. ::: .6 A LICHTENSTEIN, 1948 o MI[MAN.1958. 1960 ..• 5 o .. 6 o [':, > .. • o o 0 s 5 8 ...... • • II: ••••• • I • • •• • .0
PERCENT-BY-WEIGHT 1.5 1.2 L , to 0.02 5.0 MOLAR ITY OF SUGAR ..~ I,D ~ • A ..~ .9 • .. .. 6 ~ .7 0 <> 6 ~ .6 0 o SORBITOL • ARABINOSE PE.NTOSES I- ., o MA"INtTOL SUGAR ALCOHOL S • XYLOSE ~ .5 ~ I.. o DULCITOL ( POLYGLyCOLS) •0 i •• II> ~ .4 o GLyCEROl • 0 • .5 0 •• .;- 0 .~ .2 eo ro o .. ::I .. ft .. ... S ...... I- ..0 .. ~ I- J... ~ ~ '" I,. i .. "...c... 3 . o . o ~ 7 , 6 • Fig. 4. Relative sweetness of sugars .. o • o • • • •• obtained in the present study and in '" o :lII: • o previously published ones. In the present CD ..~ • • study, the values for relative sweetness ..~ 3 :> were computed when concentration was a expressed both as molarity. and as per cent II: ..!i; by weight. The exponent for sweetness was o '-_"-__L-_-'--_-'-__"--o ,,.J-I_--'__---'-_-.1__.L.-__L...-.i fixed at 1.3. Estimates of relative sweetness 0.1 0.2 0.5 1.0 2.0 5.0 0.1 0.2 0.5 1.0 2.0 5.0 attributed to Deutsch-Renner and Nieman MOLARITY OF SUGAR were obtained from tabled values presented in Amerine, Pangborn, and Roessler (1965). •
D-FRUCTOSE and fructose grow at about the same rate o-SOR80SE: O-GLUCOS£ (Fig. 38). MONOSACCHARIDE 5 0- GALACTOSE D,.- "ANNeSE Relative Sweetness of Sugars \}- RHAMNOSE
The ratio ofmagnitude estimates at each 10 concentration expresses relative sweetness at that concentration. If the exponent for o: all sugar sweetness is 1.3, then the ratio of
intercepts (values of k) between pairs of <:J 0 sugars expresses their relative sweetness ~ 0'<7 , both at the concentration given by the 5 <:0 ..~ ;:: 0 "1 intercepts as well as across the entire II: .. 0 ~ C e 0 i continuum of concentration. Thus, if one 0 3
exponent suffices, then relative sweetness ~ 2 1 remains constant, as Eq. I indicates: !
3 0 , , I , J Sugar A: Sweetness SA = kAC1. 0.1 0.2 0.5 '.0 2.0 '.0 MOLARITY OF SUGAR Sugar B: Sweetness Sa = kaCl.3 (I) C Relative sweetness is the ratio of Fig. 5. Behavior of the interquartile range of magnitude esti magnitude estimates at one concentration: mates of the sweetness of (A) oligosaccharides, (B) pentoses and sugar alcohols, and (C) monosaccharides after modulus equali· zation was done to remove differences in the moduli used by different Os, The unit of variability is the decilog (10th of a With one representative exponent, the logarithmic unit). .
Perception & Psychophysics, 1970, Vol. 7 (5) 319 m sweetness functions become parallel lines Sugar A: Sweetness SA = kAC LANE, H. C•• CATANIA, A. C., & STEVENS, S. in log-log coordinates. separated by a S. Voice level: Autophonic scale. perceived constant distance that corresponds to a n loudness, and effects of sidetone. Iournal of Sugar B: Sweetness SB :: kBC n,;: m (3) the Acoustical Society of America, 1960, 32. fixed ratio. Table 3 lists the absolute and 1337-13"4. n relative intercepts (sucrose :: 1.0). assuming Relative Sweetness = SA/SB:: kAcm/kBc LAWRENCE, A. R., & FERGUSON, L. N. the exponent to be 1.3. The intercepts Exploratory physiochemicai studies on the were obtained by a least-squares fit, in ::kAlkBxcm-n sense of taste. Nature, 1959. 183, 1469-1471. LICHTENSTEIN, P. E. The relative sweetness of which the exponent was fixed at 1.3. sugars: Sucrose lIIId dextrose. Iournal of Whether measured in terms of molarity Instead of traveling in parallel paths, Experimental Psychology, 1948. 38, 578-580. or per cent by weight, sucrose and fructose separated by a constant distance. the MOSKOWITZ. H. R. Scales of intensity for single are the sweetest sugars (Fig. 4), whereas for functions for pairs of sugars cross, so that and compound tastes. Unpublished doctoral dissertation. Harvard University, 1968. the remaining sugars, the measure of the logarithmic distance (i.e., ratio) PANEK. D. W•• &. STEVENS, I. C. Psychofit. a concentration influences the order of continually changes with concentration. computer program for the treatment of relative sweetness. When molarity is used. psychophysical data. Laboratory of the heavier sugars (oligosaccharides), such Vuiability of Mapitude Estimates Psychophysics. Harvard University, 1965, PPR 315. as maltose and lactose, are sweeter than the Figure 5 shows how one measure of PANGBORN. R. M. Relative taste intensities of lighter monosaccharides, whereas with per variability, the interquartile range, behaves selected sugars and organic acids. Iournal of cent by weight, the order is reversed. This for different sugars. The statistic was Food Science, 1963,28,726-733. finding is intuitively meaningful, because computed from the logarithms of the PANGBORN, R. M., s CHRISP, R. B. Gustatory molarity pits light sugars (e.g., glycerol) magnitude estimates after the scale sizes responses to anomeric sugars. Experientia, 1966.22,612-615. against much heavier ones (e.g., raffinose] were equated by modulus equalization. PANGBORN, R. M.. &. GEE, S. Relative without allowing for the differences in Each point is a weighted value, obtained sweetness of a and {J forms of selected sugars. weight. On the other hand, per cent by from several experiments. with weights Nature, 1961,191,810-811. weight assesses the amount of solute in proportional to the number of judgments PAUL, T. Physfkalische Chemie der Le bensmittel: V. Der Siissungrade der solution, regardless ofits molecular weight. obtained in each experiment. In general. Sasstoffe. Zeitschrift fUr Elektrochemje, 1921, Values for dulcitol and raffinose are the variability behavesin a familiar pattern. 27,539-546. more tentative than are the rest, because At low concentrations, the interquartile STEVENS. I. C. A comparison of ratio scales for neither sugar ever becomes sufficiently range is relatively high, but it stabilizes the loudness of white noise and the brightness sweet to determine a good sweetness over the top 80% of the stimulus of white light. Unpublished doctoral dissertation, Harvard University, 1957. function with many points. continuum. A similar pattern occurs for STEVENS. S. S. The psychophysics of sensory the variability of matches of numbers and function. American Scientist, 1960, 48, Relative Sweetness from Other Studies noise to the intensity of taste and of taste 226-253. The results of other studies were mixtures (Moskowitz, 1968). STEVENS. S. S. Sensory scales of taste intensity. analyzed to determine relative sweetness. Perception & Psychophysics, in press. If the interquartile range of the STEVENS, S. S., & STEVENS, I. C. Dynamics of The pairs of concentrations of sugars judgments (in logarithmic units called visual brightness. Unpublished monograph, matching in sweetness were substituted in decilogs) is constant, then the variability of Laboratory of Psychophysics, Harvard Eq. 1; the two parts were set equal, and the the judgments is proportional to the mean University. 1960, PPR 246. equation was solved for the ratio of judgment. This stability of relative intercepts (under the assumption that the variability reaffirms Weber's law, which sweetness exponent was 1.3). There is a posits that the variability of sensory spread of values (Fig. 4) for the relative judgments is relative and increases with sweetness of sugars, especially for glucose. increasing intensity. Some of the variability can be traced to NOTES different procedures used by the different 1. Research supported in part by a National REFERENCES Science Foundation predoctoral fellowship and Es, but the remainder may be attributable AMERINE, M., PANGBORN, R., & ROESSLER, to differences of the sweetness exponents in part by National Institute of Health grant to E. Principles of sensory evaluation of food. Harvard University (Laboratory of Psychophysics of different sugars. If. for example, the New York: Academic Press, 1965. Report PPR-35 I). sweetness exponent ofglucose exceeds that CAMERON, A. T. The taste sense and the 2. Current address: U.S. Army Natick of sucrose, then their relative magnitude relative sweetness of sugar and other sweet Laboratories, Pioneering Research Laboratories. substances. Scientific Reports of the Sugar Natick. Mass. 01760. estimates will differ across concentrations. Research Foundation, No.9, New York, 1947. Rather than one representative value. there sucrose intensity. Perceptual & Motor Skills, (Accepted for publication September 30, 1969.; will be an entire distribution (Eq. 3): 1965, 20. 294.
320 Perception & Psychophysics, 1970. Vol. 7 (5)