a r X i v :a s t r o -p h /0011325v 1 16 N o v 2000On the Size-Dependence of the Inclination Distribution of the
Main Kuiper Belt
Harold F.Levison
and
S.Alan Stern Department of Space Studies,Southwest Research Institute,Boulder,CO 80302ABSTRACT We present a new analysis of the currently available orbital elements for the known Kuiper belt objects.In the non-resonant,main Kuiper belt we ?nd a statistically signi?cant relationship between an object’s absolute magnitude (H )and its inclination (i ).Objects with H <6.5(i .e .radii ～>170km for a 4%albedo)have higher inclinations than those with H >6.5(radii ～<170km).We have shown that this relationship is not caused by any obvious observational bias.We argue that the main Kuiper belt consists of the superposition of two distinct distributions.One is dynamically hot with inclinations as large as ～35?and absolute magnitudes as bright as 4.5;the other is dynamically cold with i ～<5?and H >6.5.The dynamically cold population is most likely dynamically primordial.We speculate on the potential causes of this relationship.Subject headings:solar system:general,Kuiper Belt,formation
1.Introduction
The discovery of the Kuiper belt in1992(Jewitt&Luu1993)issued in a new era for the study of the outer solar system.The Kuiper belt is important not only because it is a rich, new region of the solar system to be explored,but because it contains important fossil clues about the formation of the outer solar system in particular,and about planet formation in general.
Since its discovery,the Kuiper belt has supplied us with surprise after surprise.For example,before it was discovered,theorists believed that the Kuiper belt would consist of objects on low-inclination,nearly-circular orbits beyond the orbit of Neptune(Levison &Duncan1993;Holman&Wisdom1993).This belief seemed to be con?rmed with the discovery of the?rst two Kuiper Belt Objects(hereafter KBOs),1992QB1and1993FW. However,the next four objects discovered revealed a real surprise.At the time of discovery their heliocentric distances were close enough to Neptune’s orbit that their orbits should be unstable,unless protected by some dynamical mechanism.Indeed,many believed that they might have been Neptunian Trojans.However,these were the?rst discoveries of an unexpected population of objects on highly eccentric(up to0.3)orbits in the2:3mean motion resonance with Neptune(co-orbiting with Pluto).
Currently,objects in the trans-Neptunian region are divided into two main groups(see Malhotra et al.2000for a review).The Kuiper belt consists of objects that are primarily on long-lived orbits,while the scattered disk consists of objects that have su?ered a close encounter with Neptune(Duncan&Levison1997;Luu et al.1997).The Kuiper belt itself is typically subdivided into two populations.Inside of roughly42AU,objects tend to be locked into mean motion resonances with Neptune.Most known objects in this class are in Neptune’s2:3mean motion resonance.However,a fraction also reside in the3:5and the 3:4resonances.The orbits of all these objects are probably a result of resonance capture during the slow outward migration of Neptune during the late stages of planet formation (Malhotra1995).
Beyond42AU,although several objects are believed to be in the1:2mean motion resonance(Marsden2000a),most objects are not on resonant orbits.These non-resonant objects are members of what has come to be called the main Kuiper belt.Models of planetary migration(e.g.Malhotra1995;Holman1995;Hahn&Malhotra1999)predict that unlike the KBOs in mean motion resonances,main KBOs should be on relatively low-inclination, nearly-circular orbits.However,recent observations have shown that this is not the case.
Numerous objects in this region have very large inclinations1,certainly up to about32?,and most likely even higher(Marsden2000a).
Several papers have been published which attempt,among other things,to explain the high inclinations seen in the main Kuiper belt.The mechanisms invoked to date involve the scattering of KBOs by large objects temporarily evolving through the region.It takes a massive object to excite KBOs to high inclination;much more massive than the KBOs themselves2.Petit et al.(1999)suggest that the dynamically excited Kuiper belt is caused by the passage of Earth-mass objects through that region of the solar system.Thommes et al.(1999)suggest that the large inclinations are due to the passage of Uranus and/or Neptune through the Kuiper belt while on eccentric orbits,after these planets were ejected from the region between Jupiter and Saturn.Ida et al.(2000)suggest that the Kuiper belt was excited by a passing star.
In this paper we present an analysis of the currently available orbital data of main belt KBOs which shows a new and surprising trend—an unexpected and intriguing correlation between inclination and absolute magnitude.In particular intrinsically bright objects tend to be found on larger inclinations than do intrinsically faint objects.In§2we present the data and discuss the statistical signi?cance of this trend.In§3we investigate whether this trend is a result of observational selection e?ects.Our preliminary interpretation of this trend is presented in§4.We summarize our?ndings in§5.
2.Observations
The KBO orbital elements we employ here were taken from the Minor Planet Center’s web site(https://www.doczj.com/doc/3c11098497.html,/cfa/ps/lists/TNOs.html for October20,2000; Marsden2000a).Before we describe our results,however,we?rst caution the reader about the use of such data.Although the orbital elements in this dataset are given to several signi?cant?gures,many of them are uncertain,and signi?cant changes for individual objects routinely occur as more data is collected.This is particularly severe for objects that have been observed for only one season(B.Marsden,https://www.doczj.com/doc/3c11098497.html,m.).Thus,we restrict our analysis to objects that have been observed over multiple oppositions.There are124such objects in our dataset;roughly a third of the total.
In general,the inclination,i,is the best determined of the6orbital elements because it is uniquely determined by the motion of KBO perpendicular to the ecliptic.For an object in the ecliptic and at opposition(where most KBOs have been discovered),observations taken over even just a short period of time allow for a determination of its instantaneous heliocentric distance,but do not allow for a unique determination of the semi-major axis,a, or eccentricity,e.However,since the instantaneous heliocentric distance is well determined (being directly calculated from the observed rate of motion),we do have a good estimate of the object’s absolute magnitude(H).3
It also should be noted that the MPC dataset su?ers from a host of observational selection e?ects,including those that a?ect inclination.Surveys for KBOs tend to search near the ecliptic and thus there is a strong selection against objects with large inclinations. Analysis of this and other observational biases is complicated by the fact that these objects were discovered by many di?erent observing teams using di?erent equipment and di?erent search methods.Thus,the observational biases and limiting magnitudes vary from object to object.This complication makes it di?cult to statistically analyze the KBO orbital dataset for trends.We return to this issue in§3.
Since many objects in mean motion resonances have had their inclinations a?ected by these resonances,we restrict ourselves to objects in the main Kuiper belt.We de?ne members of the main Kuiper belt as those objects with a>42.5AU(outside Neptune’s 3:5mean motion resonance)and e<0.2(to avoid objects in Neptune’s1:2mean motion
resonance and the scattered disk;Duncan&Levison1997)4.There are80objects that meet these criteria.
Figure1shows the inclinations of these objects as a function of their absolute magni-tude.The inclinations in this?gure are accurate to better than±0.5?,while the absolute magnitudes are accurate to about±0.5magnitudes(B.Marsden,https://www.doczj.com/doc/3c11098497.html,m.).Notice that this?gure indicates a distinct di?erence in the character of the inclinations for objects that have H<6.5compared to those with H>6.5.In order to further illustrate this point,we provide Figure2,which shows the cumulative inclination distribution for the two populations.We refer to the absolute magnitude boundary between these groups as H break.
The natural conclusion from Figures1and2is that the inclination distribution of the intrinsically faint(H>6.5)objects appears to be signi?cantly lower than the intrinsically bright objects.Indeed,the median inclination of the faint objects is2.2?,but the median inclination of the bright objects is12?.Of course,assuming that there is no systematic variation of KBOs albedos,the intrinsically bright objects represent the largest KBOs5. Thus,Figures1and2suggest that the largest of the objects in the main Kuiper belt are more dynamically excited than smaller objects.This result is surprising because the mechanisms thus far suggested for exciting the Kuiper belt(see§1)have predicted such a behavior(however see Thommes et al.2000).Because in each of these scenarios the perturber that excites the Kuiper belt is much larger than the KBOs,the response of a KBO to the perturber should be virtually independent of its size.
Before we discuss our interpretation of our new result,we?rst wish to demonstrate that this?nding is statistically signi?cant.After all,there are only8objects in our sample with H<6.5,so in principle,small number statistics could be responsible for this result.In order to address this issue we employ the Kolmogorov-Smirnov(K-S)statistical test(Press et al.1992),which calculates the probability that two distributions are derived from the same parent distribution,where a zero probability means the distributions are dissimilar,and unit probability means they are the same.We?nd that the K-S probability of the two inclination distributions seen in Figure2is0.03.Thus,it is unlikely that the two distributions are the same6,and we can rule out that the two populations are the same at the97%con?dence
level.
We must also be careful so as to not fortuitously choose a value of the transition absolute magnitude,H break(set to6.5above),which happens to give a low value of the K-S probability. So,in Figure3we present the K-S probability as a function of H break.This?gure shows that the K-S probability is small for all values of H break<6.5,but becomes large for values fainter than this.This result can be understood by considering Figure1.If H break<6.5,we have only dynamically hot objects in the bright population,and since one is only adding a few dynamically hot objects to the faint group,the inclination distribution of the two groups remain roughly unchanged.If H break>6.5,one starts adding dynamically cold faint objects to the bright group.Since the cold population far outnumbers the hot bright population, cold objects start to dominate the bright group as H break becomes larger than6.5.So,the two distributions look similar.
In short,Figure3shows that our choice of H break=6.5is not just fortuitous and does not lead us to a false conclusion about the statistical signi?cance of our?nding.Thus,we conclude that objects with intrinsic brightnesses greater than H break=6.5actually do have an inclination distribution that is statistically di?erent from that of fainter objects.
Could dynamical friction or physical collisions signi?cantly modify an inclination distri-bution where the large objects have higher inclinations?The response timescale(Binney& Tremaine1987)of large KBOs to dynamical friction in a dynamically cold,ancient Kuiper belt of50M⊕(see Stern1996)is～109years.However,after dynamical excitation to eccentricities and inclinations characteristic of the present-day Kuiper belt,this timescale increases to～>1012years.The lower mass of the Kuiper Belt which exists today increases this timescale to～>1014years.A second potential way of modifying inclinations is through physical collisions.However,the time required for a100-km class KBO to impact a signi?-cant fraction of its own mass in a50M⊕Kuiper belt is also of order～109years.Since we estimate that both the dynamical and collisional relaxation timescales are of order100times longer than the time required for an excited,massive KB to erode due to collisions(Stern &Colwell1997),one must conclude that the dynamical con?guration of the ancient objects in the present-day,main Kuiper belt is a well-preserved,fossil remnant of the excitation event(s)itself.
3.Regarding Potential Observational Biases
In this section we investigate whether the di?erences seen in the inclination distributions of the bright and faint main Kuiper belt objects could be the result of observational biases. As we described above,this is a di?cult issue because these objects were discovered with a variety of instrumentation and under a variety of observing conditions.In particular,the surveys that discovered the faint objects tend to have limited sky coverage,so they would not have found the bright objects,which are rare.On the other hand,the surveys that covered the most sky have fairly bright limiting magnitudes,so they would not have discovered the faint objects.Our task is made still more di?cult because many surveys remain unpublished, and the details of how these discoveries were made are unknown.
Here we investigate the only two possible observational selection e?ects that we could think of that could erroneously lead us to the results of the last section.First,as we described above,the faint objects tend to be discovered by di?erent surveys than the bright objects. The probability of discovering an object of a particular inclination is a strong function of the ecliptic latitude of the discovery images.Images taken at high ecliptic latitude cannot discover low inclination objects.On the other hand,images taken at low ecliptic latitude are biased against discovering high inclination objects.
The results shown in Figures1and2could be a result of di?erences in the ecliptic latitude of the discovery images.For example,if the surveys that covered a large area of the sky tend to stray further from the ecliptic,we might see the type of distributions seen in Figures1and2.Figure4shows the ecliptic latitude of the objects in our sample at the time of their discovery as a function of their absolute magnitude.This data shows that the bright objects tend to be found at the same ecliptic latitudes as the faint objects.Indeed, we performed a K-S test similar to that above using ecliptic latitude instead of inclination and found the K-S probability is larger than0.5for all values of H break.Thus,the?ndings discussed in§2cannot be explained away by discovery selection e?ects.
Selection e?ects on the recovery of objects could also in principle erroneously lead to the results obtained in§2.It is well known that the brightest KBOs attract more followup observations then the faint ones.This is because the faint objects require large telescopes on which it is di?cult to obtain observing time.As such the fainter objects tend to be preferentially lost.Of the objects in the main belt discovered before the year2000(so there was opportunity for them to have been observed during a second opposition),all the objects with H<5.5have been recovered,while only36%of the objects with H>7.5have been observed again.If,for the faint objects,there is a selection against recovering high inclination objects,then the?ndings of§2could be in error.To check this possibility,Figure5shows the fraction of main belt KBOs fainter than6.5that have been recovered as a function of
their inclination.We only include those objects that have discovered before the year2000. The error-bars represent the error in the mean;they increase in size with inclination because there are fewer high inclination objects.Note that the recovery fraction for these objects is independent of inclination.Thus,the?nding that objects with H<6.5tend to have larger inclinations than objects with H>6.5is also not a result of recovery statistics.
4.Interpretation
Perhaps the most natural interpretation for the data in Figure1is that we are seeing the superposition of two distinct populations.The?rst population contains dynamically hot objects with inclinations up to～35?and absolute magnitudes as bright as4.5.(Of course in the future,members of this hot population that are larger and/or have higher inclinations than those currently known,may well be discovered.)The other population is a dynamically cold one with i～<5?and H～>6.5(radii～<170for albedo of4%).
There are two lines of supporting evidence in our dataset for two distinct populations. First,so far in this discussion we have restricted ourselves to the analysis of inclinations only.However,in a dynamically isotropic system,the root-mean-square(RMS)of the ec-centricities should be approximately twice the RMS of the sine of the inclinations(Lissauer &Stewart1993).So,if our‘dynamically cold’population is real,the eccentricities should also be small.Indeed,eccentricities should be so small that the eccentricity distribution of this population should not be truncated by Neptune.The RMS of the sine of the inclination of objects fainter than H=6.5and with i≤5?is0.039,which predicts that the RMS eccentricity should be0.078.It is observed to be0.076which is in good agreement.The RMS eccentricity of the remaining main belt objects is0.11,which is signi?cantly larger. Thus,our dynamically cold population appears to be real.
Our interpretation is also supported by Figure6,which is the same as Figure2,but with the H>6.5curve scaled so that the two curves cross at i=5?.Note that the two distributions are the same for i>5?,arguing that they are members of the same population. So,we can conclude from this that the intrinsically faint objects with i>5?are part of the same population as the intrinsically bright objects.If this interpretation is correct, then approximately40%of the objects in our sample are part of the dynamically excited population.
As we were preparing this manuscript,two papers became available that also argue for two populations in the main Kuiper belt.Brown(2000)performed detailed modeling of the one-dimensional inclination distribution of the main Kuiper belt.Although his results are somewhat model dependent,owing to an assumed functional form for the intrinsic inclination distribution of sin(i)exp(?i2/2σ2),he concludes that the main Kuiper belt is most likely composed of the superposition of two distinct populations—one dynamically hot and the other dynamically cold.The dynamically cold population is best?t byσ=2.2?,which is consistent with our estimate that the maximum inclination of this population is roughly5?.
More convincing and relevant,however,are the recent results of Tegler&Roman-ishin(2000),who have studied the colors of KBOs.It has been previously shown that the
Kuiper belt and scattered disk most likely contain two distinct color populations—one that is comprised of objects that are gray in color and one in which the objects are red(Tegler &Romanishin1998).Tegler&Romanishin(2000)found that in the main Kuiper belt,all objects on low-inclination,nearly-circular orbits are red in color,while the rest of the KBOs are a mixture of both red and gray colors(also see Marsden2000b).The black and red dots in Figure1represent those objects for which Tegler&Romanishin measured a gray and red color,respectively.Tegler&Romanishin’s result seems to indicate that at least the surfaces of the dynamically cold main Kuiper belt objects are chemically distinct as a group from the rest of the KBOs.
Based on the various lines of evidence we conclude that the main Kuiper belt is a superposition of two distinct populations and that these populations consist of objects with di?erent sizes,di?erent dynamics,and di?erent surface properties.We speculate that a natural explanation for this result is as follows7.
Initially the protoplanetary disk in the Uranus-Neptune region and beyond was dy-namically cold with size distribution and color that varied with heliocentric distance.In particular,signi?cant numbers of large objects(H<6.5)had only formed in the inner re-gions of the disk while few,if any,objects this large formed in the outer regions.Then a dynamically violent event cleared the inner region of the disk,dynamically scattering the inner-disk objects outward.Most of these objects were either ejected from the solar system, placed in the Oort cloud,or became members of the scattered disk.However,a few of these objects would have been deposited in the main Kuiper belt,becoming the dynamically hot population described above.
This scenario has several implications.First,it suggests that objects in the scattered disk,the dynamically hot main Kuiper belt,and perhaps in Neptune’s mean motion reso-nances should have similar size-distributions and physical characteristics because they were all populated with the objects initially in the inner disk.In addition,since current models of the Kuiper belt show that the cold population is likely to be dynamically stable(Dun-can et al.1995),this population should not be contributing signi?cantly to the Centaurs. Hence,the Centaurs should also have a size-distribution and physical properties similar to the dynamically hot main Kuiper belt and its cohorts.This appears to be born out by observations.Tegler&Romanishin(2000)?nd that the scattered disk,the dynamically hot main Kuiper belt,the plutinos,and the Centaurs roughly have the same mixture of red and gray objects.In addition,all these regions contain objects with H<6.5.
Our scenario also suggests that the dynamically cold population is a dynamically pri-mordial population;member objects most likely formed near where they are observed and have not been signi?cantly perturbed over the age of the solar system.8It also suggests that because the intrinsically brightest objects in this population have H～6.5and other brighter(larger)objects have been found in the main Kuiper belt,that the largest object to grow in this region has H=6.5or a radius of～170km(4%albedo).This result may supply important constraints on the accretional history of this region,possibly includ-ing coonstraints on the solid surface density of material in the region and the date of the event(s)that dynamically excited the Kuiper belt.
5.Summary
We have shown that the inclination distribution of objects in the main Kuiper belt most likely varies as a function of absolute magnitude.In particular,objects intrinsically brighter than H=6.5appear to have systematically higher inclinations than intrinsically fainter objects.There is only～3%chance that these two distributions are the same.We have shown that this result is unlikely to be caused by biases in discovery or recovery observing procedures.Therefore,although it is possible that this conclusion is a result of small number statistics,we believe that it is real.Future discoveries and followups will clearly resolve this issue.The clear implication of our result is that a main belt object’s inclination is dependent on its size.
The di?erences between intrinsically bright objects and the intrinsically faint objects is best seen in Figure1.Perhaps the most natural interpretation for the data in this?gure is that we are seeing the superposition of two distinct populations.The?rst contains a dynamically hot population(inclinations up to～35?)consisting of both large and small objects(absolute magnitudes as small as4.5or radii up to～330km for albedos of4%). Indeed,even larger objects and/or objects with higher inclinations are likely to still be found.The other population is a dynamically cold one(i～<5?)preferentially containing smaller objects(H～>6.5or radii～<170km for albedos of4%).
We would like to thank L.Dones,B.Gladman,and P.Tamblyn for useful discussions. We are also grateful to W.Bottke,R.Canup,M.Duncan and an anonymous referee for comments on an early version of this manuscript.We also thank NASA’s PGG and Origins programs for support.
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Fig. 1.—The inclination(i),absolute magnitude(H)distribution of multiple opposition objects in the main Kuiper belt as of October20,2000.Note that objects brighter than H=6.5are dynamically more excited than those with H>6.5.The red dots represent red objects for which Tegler&Romanishin(2000)measured a V-R>0.6.The black dots represent gray objects for which they measured a V-R<0.6.The blue dots represent objects for which they have not measured colors.
Fig. 2.—The cumulative inclination distribution for members of the main Kuiper belt with multiple opposition orbits.The population is divided into two groups.The solid curve shows only those objects fainter than H=6.5,while the dotted curve only includes objects brighter then this.A K-S test puts the probability that these two distributions are the same at0.03.
Fig. 3.—The K-S probability that the inclination distribution of objects brighter than H break is the same as that of objects less than H break.The K-S probability is small for H break<6.5indicating that the two distributions are indeed most likely di?erent.
Fig.4.—The ecliptic latitude,absolute magnitude(H)distribution of multiple opposition objects in the main Kuiper belt as of October20,2000.The ecliptic latitude was calculated at the time of discovery.Note that there is not a signi?cant correlation between these two parameters.
Fig. 5.—The fraction of main belt H>6.5KBOs that have so far been recovered as a function of their inclination.We only include those objects that have had the potential for being observed on multiple oppositions.The error-bars represent the error in the mean. Fig. 6.—The same as Figure2except that the H>6.5curve is scaled so that the two curves cross at i=5?.
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【摘要】黄自先生是我国杰出的音乐家，他以艺术歌曲的创作最为代表。而黄自先生特别强调了钢琴伴奏对于艺术歌曲组成的重要性。本文是以黄自先生创作的具有爱国主义和人道主义的艺术歌曲《天伦歌》为研究对象，通过对作品分析，归纳钢琴伴奏的弹奏方法与特点，并总结黄自先生的艺术成就与贡献。 【关键词】艺术歌曲；和声；伴奏织体；弹奏技巧 一、黄自艺术歌曲《天伦歌》的分析 （一）《天伦歌》的人文及创作背景。黄自的艺术歌曲《天伦歌》是一首具有教育意义和人道主义精神的作品。同时，它也具有民族性的特点。这首作品是根据联华公司的影片《天伦》而创作的主题曲，也是我国近代音乐史上第一首为电影谱写的艺术歌曲。作品创作于我国政治动荡、经济不稳定的30年代，这个时期，这种文化思潮冲击着我国各个领域，连音乐艺术领域也未幸免――以《毛毛雨》为代表的黄色歌曲流传广泛，对人民大众，尤其是青少年的不良影响极其深刻，黄自为此担忧，创作了大量艺术修养和文化水平较高的艺术歌曲。《天伦歌》就是在这样的历史背景下创作的，作品以孤儿失去亲人的苦痛为起点，发展到人民的发愤图强，最后升华到博爱、奋起的民族志向，对青少年的爱国主义教育有着重要的影响。 （二）《天伦歌》曲式与和声。《天伦歌》是并列三部曲式，为a+b+c，最后扩充并达到全曲的高潮。作品中引子和coda所使用的音乐材料相同，前后呼应，合头合尾。这首艺术歌曲结构规整，乐句进行的较为清晰，所使用的节拍韵律符合歌词的特点，如三连音紧密连接，为突出歌词中号召的力量等。 和声上，充分体现了中西方作曲技法融合的创作特性。使用了很多七和弦。其中，一部分是西方的和声，一部分是将我国传统的五声调式中的五个音纵向的结合，构成五声性和弦。与前两首作品相比，《天伦歌》的民族性因素增强，这也与它本身的歌词内容和要弘扬的爱国主义精神相对应。 （三）《天伦歌》的伴奏织体分析。《天伦歌》的前奏使用了a段进唱的旋律发展而来的，具有五声调性特点，增添了民族性的色彩。在作品的第10小节转调入近关系调，调性的转换使歌曲增添抒情的情绪。这时的伴奏加强和弦力度，采用切分节奏，节拍重音突出，与a段形成强弱的明显对比，突出悲壮情绪。 c段的伴奏采用进行曲的风格，右手以和弦为主，表现铿锵有力的进行。右手为上行进行，把全曲推向最高潮。左手仍以柱式和弦为主，保持节奏稳定。在作品的扩展乐段，左手的节拍低音上行与右手的八度和弦与音程对应，推动音乐朝向宏伟、壮丽的方向进行。coda 处，与引子材料相同，首尾呼应。 二、《天伦歌》实践研究 《天伦歌》是具有很强民族性因素的作品。所谓民族性，体现在所使用的五声性和声、传统歌词韵律以及歌曲段落发展等方面上。 作品的整个发展过程可以用伤感――悲壮――兴奋――宏达四个过程来表述。在钢琴伴奏弹奏的时候，要以演唱者的歌唱状态为中心，选择合适的伴奏音量、音色和音质来配合，做到对演唱者的演唱同步，并起到连接、补充、修饰等辅助作用。 作品分为三段，即a+b+c+扩充段落。第一段以五声音阶的进行为主，表现儿童失去父母的悲伤和痛苦，前奏进入时要弹奏的使用稍凄楚的音色，左手低音重复进行，在弹奏完第一个低音后，要迅速的找到下一个跨音区的音符；右手弹奏的要有棱角，在前奏结束的时候第四小节的t方向的延音处，要给演唱者留有准备。演唱者进入后，左手整体的踏板使用的要连贯。随着作品发展，伴奏与旋律声部出现轮唱的形式，要弹奏的流动性强，稍突出一些。后以mf力度出现的具有转调性质的琶音奏法，要弹奏的如流水般连贯。在重复段落，即“小
一般过去式 时间状语：yesterday just now (刚刚) the day before three days ag0 a week ago in 1880 last month last year 1. I was in the classroom yesterday. I was not in the classroom yesterday. Were you in the classroom yesterday. 2. They went to see the film the day before. Did they go to see the film the day before. They did go to see the film the day before. 3. The man beat his wife yesterday. The man didn’t beat his wife yesterday. 4. I was a high student three years ago. 5. She became a teacher in 2009. 6. They began to study english a week ago 7. My mother brought a book from Canada last year. 8.My parents build a house to me four years ago . 9.He was husband ago. She was a cooker last mouth. My father was in the Xinjiang half a year ago. 10.My grandfather was a famer six years ago. 11.He burned in 1991
我国艺术歌曲钢琴伴奏-精 2020-12-12 【关键字】传统、作风、整体、现代、快速、统一、发展、建立、了解、研究、特点、突出、关键、内涵、情绪、力量、地位、需要、氛围、重点、需求、特色、作用、结构、关系、增强、塑造、借鉴、把握、形成、丰富、满足、帮助、发挥、提高、内心 【摘要】艺术歌曲中，伴奏、旋律、诗歌三者是不可分割的重 要因素，它们三个共同构成一个统一体，伴奏声部与声乐演唱处于 同样的重要地位。形成了人声与器乐的巧妙的结合，即钢琴和歌唱 的二重奏。钢琴部分的音乐使歌曲紧密的联系起来，组成形象变化 丰富而且不中断的套曲，把音乐表达的淋漓尽致。 【关键词】艺术歌曲；钢琴伴奏；中国艺术歌曲 艺术歌曲中，钢琴伴奏不是简单、辅助的衬托，而是根据音乐 作品的内容为表现音乐形象的需要来进行创作的重要部分。准确了 解钢琴伴奏与艺术歌曲之间的关系,深层次地了解其钢琴伴奏的风 格特点,能帮助我们更为准确地把握钢琴伴奏在艺术歌曲中的作用 和地位，从而在演奏实践中为歌曲的演唱起到更好的烘托作用。 一、中国艺术歌曲与钢琴伴奏 “中西结合”是中国艺术歌曲中钢琴伴奏的主要特征之一，作 曲家们将西洋作曲技法同中国的传统文化相结合，从开始的借鉴古 典乐派和浪漫主义时期的创作风格，到尝试接近民族乐派及印象主 义乐派的风格，在融入中国风格的钢琴伴奏写作，都是对中国艺术 歌曲中钢琴写作技法的进一步尝试和提高。也为后来的艺术歌曲写 作提供了更多宝贵的经验，在长期发展中，我国艺术歌曲的钢琴伴 奏也逐渐呈现出多姿多彩的音乐风格和特色。中国艺术歌曲的钢琴
写作中，不可忽略的是钢琴伴奏织体的作用，因此作曲家们通常都以丰富的伴奏织体来烘托歌曲的意境，铺垫音乐背景，增强音乐感染力。和声织体，复调织体都在许多作品中使用，较为常见的是综合织体。这些不同的伴奏织体的歌曲，极大限度的发挥了钢琴的艺术表现力，起到了渲染歌曲氛围，揭示内心情感，塑造歌曲背景的重要作用。钢琴伴奏成为整体乐思不可缺少的部分。优秀的钢琴伴奏织体，对发掘歌曲内涵，表现音乐形象，构架诗词与音乐之间的桥梁等方面具有很大的意义。在不断发展和探索中，也将许多伴奏织体使用得非常娴熟精确。 二、青主艺术歌曲《我住长江头》中钢琴伴奏的特点 《我住长江头》原词模仿民歌风格，抒写一个女子怀念其爱人的深情。青主以清新悠远的音乐体现了原词的意境，而又别有寄寓。歌调悠长，但有别于民间的山歌小曲；句尾经常出现下行或向上的拖腔，听起来更接近于吟哦古诗的意味，却又比吟诗更具激情。钢琴伴奏以江水般流动的音型贯穿全曲，衬托着气息宽广的歌唱，象征着绵绵不断的情思。由于运用了自然调式的旋律与和声，显得自由舒畅，富于浪漫气息，并具有民族风味。最有新意的是，歌曲突破了“卜算子”词牌双调上、下两阕一般应取平行反复结构的惯例，而把下阕单独反复了三次，并且一次比一次激动，最后在全曲的高音区以ff结束。这样的处理突出了思念之情的真切和执著，并具有单纯的情歌所没有的昂奋力量。这是因为作者当年是大革命的参加者，正被反动派通缉，才不得不以破格的音乐处理，假借古代的
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高中英语~词性~句子成分~语法构成 第一章节：英语句子中的词性 1.名词：n. 名词是指事物的名称，在句子中主要作主语.宾语.表语.同位语。 2.形容词;adj. 形容词是指对名词进行修饰~限定~描述~的成份，主要作定语.表语.。形容词在汉语中是（的）.其标志是: ous. Al .ful .ive。. 3.动词：vt. 动词是指主语发出的一个动作，一般用来作谓语。 4.副词：adv. 副词是指表示动作发生的地点. 时间. 条件. 方式. 原因. 目的. 结果.伴随让步. 一般用来修饰动词. 形容词。副词在汉语中是（地）.其标志是：ly。 5.代词：pron. 代词是指用来代替名词的词，名词所能担任的作用，代词也同样.代词主要用来作主语. 宾语. 表语. 同位语。 6.介词：prep.介词是指表示动词和名次关系的词，例如：in on at of about with for to。其特征：
介词后的动词要用—ing形式。介词加代词时，代词要用宾格。例如：give up her（him）这种形式是正确的，而give up she（he）这种形式是错误的。 7.冠词：冠词是指修饰名词，表名词泛指或特指。冠词有a an the 。 8.叹词：叹词表示一种语气。例如：OH. Ya 等 9.连词：连词是指连接两个并列的成分，这两个并列的成分可以是两个词也可以是两个句子。例如：and but or so 。 10.数词：数词是指表示数量关系词，一般分为基数词和序数词 第二章节：英语句子成分 主语：动作的发出者，一般放在动词前或句首。由名词. 代词. 数词. 不定时. 动名词. 或从句充当。 谓语：指主语发出来的动作，只能由动词充当，一般紧跟在主语后面。 宾语：指动作的承受着，一般由代词. 名词. 数词. 不定时. 动名词. 或从句充当. 介词后面的成分也叫介词宾语。 定语：只对名词起限定修饰的成分，一般由形容
M A: Has the case been closed yet? B: No, the magistrate still needs to decide the outcome. magistrate n.地方行政官，地方法官，治安官 A: I am unable to read the small print in the book. B: It seems you need to magnify it. magnify vt.１．放大，扩大；２．夸大，夸张 A: That was a terrible storm. B: Indeed, but it is too early to determine the magnitude of the damage. magnitude n.１．重要性，重大；２．巨大，广大 A: A young fair maiden like you shouldn’t be single. B: That is because I am a young fair independent maiden. maiden n.少女，年轻姑娘，未婚女子 a.首次的，初次的 A: You look majestic sitting on that high chair. B: Yes, I am pretending to be the king! majestic a.雄伟的，壮丽的，庄严的，高贵的 A: Please cook me dinner now. B: Yes, your majesty, I’m at your service. majesty n.１．［Ｍ－］陛下（对帝王，王后的尊称）；２．雄伟，壮丽，庄严 A: Doctor, I traveled to Africa and I think I caught malaria. B: Did you take any medicine as a precaution? malaria n.疟疾 A: I hate you! B: Why are you so full of malice? malice n.恶意，怨恨 A: I’m afraid that the test results have come back and your lump is malignant. B: That means it’s serious, doesn’t it, doctor? malignant a.１．恶性的，致命的；２．恶意的，恶毒的 A: I’m going shopping in the mall this afternoon, want to join me? B: No, thanks, I have plans already. mall n.（由许多商店组成的）购物中心 A: That child looks very unhealthy. B: Yes, he does not have enough to eat. He is suffering from malnutrition.
意见应以事实为根据. 3 来自辞典例句 192. The bombers swooped ( down ) onthe air base. 轰炸机 突袭 空军基地. 来自辞典例句 193. He mounted their engines on a rubber base. 他把他们的发动机装在一个橡胶垫座上. 14 来自辞典例句 194. The column stands on a narrow base. 柱子竖立在狭窄的地基上. 14 来自辞典例句 195. When one stretched it, it looked like grey flakes on the carvas base. 你要是把它摊直, 看上去就象好一些灰色的粉片落在帆布底子上. 18 来自辞典例句 196. Economic growth and human well - being depend on the natural resource base that supports all living systems. 经济增长和人类的福利依赖于支持所有生命系统的自然资源. 12 1 来自辞典例句 197. The base was just a smudge onthe untouched hundred - mile coast of Manila Bay. 那基地只是马尼拉湾一百英里长安然无恙的海岸线上一个硝烟滚滚的污点. 6 来自辞典例句 198. You can't base an operation on the presumption that miracles are going to happen. 你不能把行动计划建筑在可能出现奇迹的假想基础上.
英语造句大全English sentence 在句子中，更好的记忆单词！ 1、(1)、able adj. 能 句子：We are able to live under the sea in the future. (2)、ability n. 能力 句子：Most school care for children of different abilities. (3)、enable v. 使。。。能句子：This pass enables me to travel half-price on trains. 2、(1)、accurate adj. 精确的句子：We must have the accurate calculation. (2)、accurately adv. 精确地 句子：His calculation is accurately. 3、(1)、act v. 扮演 句子：He act the interesting character. （2）、actor n. 演员 句子：He was a famous actor. (3)、actress n. 女演员 句子：She was a famous actress. (4)、active adj. 积极的 句子：He is an active boy. 4、add v. 加 句子：He adds a little sugar in the milk. 5、advantage n. 优势 句子：His advantage is fight. 6、age 年龄n. 句子：His age is 15. 7、amusing 娱人的adj. 句子：This story is amusing. 8、angry 生气的adj. 句子：He is angry. 9、America 美国n.
主语+谓语 1. 理解主谓结构 1) The students arrived. The students arrived at the park. 2) They are listening. They are listening to the music. 3) The disaster happened. 2．体会状语的位置 1) Tom always works hard. 2) Sometimes I go to the park at weekends.. 3) The girl cries very often. 4) We seldom come here. The disaster happened to the poor family. 3. 多个状语的排列次序 1) He works. 2) He works hard. 3) He always works hard. 4) He always works hard in the company. 5) He always works hard in the company recently. 6) He always works hard in the company recently because he wants to get promoted. 4. 写作常用不及物动词 1. ache My head aches. I’m aching all over. 2. agree agree with sb. about sth. agree to do sth. 3. apologize to sb. for sth. 4. appear (at the meeting, on the screen) 5. arrive at / in 6. belong to 7. chat with sb. about sth. 8. come (to …) 9. cry 10. dance 11. depend on /upon 12. die 13. fall 14. go to … 15. graduate from 16. … happen 17. laugh 18. listen to... 19. live 20. rise 21. sit 22. smile 23. swim 24. stay (at home / in a hotel) 25. work 26. wait for 汉译英： 1.昨天我去了电影院。 2.我能用英语跟外国人自由交谈。 3.晚上7点我们到达了机场。 4.暑假就要到了。 5.现在很多老人独自居住。 6.老师同意了。 7.刚才发生了一场车祸。 8.课上我们应该认真听讲。9. 我们的态度很重要。 10. 能否成功取决于你的态度。 11. 能取得多大进步取决于你付出多少努力。 12. 这个木桶能盛多少水取决于最短的一块板子的长度。
【it's time to和it's time for】 ——————这其实是一个句型,只不过后面要跟不同的东西. ——————It's time to跟的是不定式（to do）.也就是说,要跟一个动词,意思是“到做某事的时候了”.如： It's time to go home. It's time to tell him the truth. ——————It's time for 跟的是名词.也就是说,不能跟动词.如： It's time for lunch.(没必要说It's time to have lunch) It's time for class.(没必要说It's time to begin the class.) They can't wait to see you Please ask liming to study tonight. Please ask liming not to play computer games tonight. Don’t make/let me to smoke I can hear/see you dance at the stage You had better go to bed early. You had better not watch tv It’s better to go to bed early It’s best to run in the morning I am enjoy running with music. With 表伴随听音乐 I already finish studying You should keep working. You should keep on studying English Keep calm and carry on 保持冷静继续前行二战开始前英国皇家政府制造的海报名字 I have to go on studying I feel like I am flying I have to stop playing computer games and stop to go home now I forget/remember to finish my homework. I forget/remember cleaning the classroom We keep/percent/stop him from eating more chips I prefer orange to apple I prefer to walk rather than run I used to sing when I was young What’s wrong with you There have nothing to do with you I am so busy studying You are too young to na?ve I am so tired that I have to go to bed early
《The Kite Runner》追风筝的人--------------------------------美句摘抄 1.I can still see Hassan up on that tree, sunlight flickering through the leaves on his almost perfectly round face, a face like a Chinese doll chiseled from hardwood: his flat, broad nose and slanting, narrow eyes like bamboo leaves, eyes that looked, depending on the light, gold, green even sapphire 翻译：我依然能记得哈桑坐在树上的样子，阳光穿过叶子，照着他那浑圆的脸庞。他的脸很像木头刻成的中国娃娃，鼻子大而扁平，双眼眯斜如同竹叶，在不同光线下会显现出金色、绿色，甚至是宝石蓝。 E.g.: A shadow of disquiet flickering over his face. 2.Never told that the mirror, like shooting walnuts at the neighbor's dog, was always my idea. 翻译：从来不提镜子、用胡桃射狗其实都是我的鬼主意。E.g.:His secret died with him, for he never told anyone. 3.We would sit across from each other on a pair of high
一、翻译 1. The idea of consciously seeking out a special title was new to me., but not without appeal. 让我自己挑选自己最喜欢的书籍这个有意思的想法真的对我具有吸引力。 2.I was plunged into the aching tragedy of the Holocaust, the extraordinary clash of good, represented by the one decent man, and evil. 我陷入到大屠杀悲剧的痛苦之中，一个体面的人所代表的善与恶的猛烈冲击之中。 3.I was astonished by the the great power a novel could contain. I lacked the vocabulary to translate my feelings into words. 我被这部小说所包含的巨大能量感到震惊。我无法用语言来表达我的感情（心情）。 4，make sth. long to short长话短说 5.I learned that summer that reading was not the innocent(简单的) pastime(消遣) I have assumed it to be., not a breezy, instantly forgettable escape in the hammock(吊床)，( though I’ ve enjoyed many of those too ). I discovered that a book, if it arrives at the right moment, in the proper season, will change the course of all that follows. 那年夏天，我懂得了读书不是我认为的简单的娱乐消遣，也不只是躺在吊床上，一阵风吹过就忘记的消遣。我发现如果在适宜的时间、合适的季节读一本书的话，他将能改变一个人以后的人生道路。 二、词组造句 1. on purpose 特意，故意 This is especially true here, and it was ~. (这一点在这里尤其准确，并且他是故意的) 2.think up 虚构，编造，想出 She has thought up a good idea. 她想出了一个好的主意。 His story was thought up. 他的故事是编出来的。 3. in the meantime 与此同时 助记：in advance 事前in the meantime 与此同时in place 适当地... In the meantime, what can you do? 在这期间您能做什么呢？ In the meantime, we may not know how it works, but we know that it works. 在此期间，我们不知道它是如何工作的，但我们知道，它的确在发挥作用。 4.as though 好像，仿佛 It sounds as though you enjoyed Great wall. 这听起来好像你喜欢长城。 5. plunge into 使陷入 He plunged the room into darkness by switching off the light. 他把灯一关，房
The effective sentences:(improve the sentences!) 1.She hopes to spend this holiday either in Shanghai or in Suzhou. 2.Showing/to show sincerity and to keep/keeping promises are the basic requirements of a real friend. 3.I want to know the space of this house and when it was built. I want to know how big this house is and when it was built. I want to know the space of this house and the building time of the house. 4.In the past ten years,Mr.Smith has been a waiter,a tour guide,and taught English. In the past ten years,Mr.Smith has been a waiter,a tour guide,and an English teacher. 5.They are sweeping the floor wearing masks. They are sweeping the floor by wearing masks. wearing masks,They are sweeping the floor. 6.the drivers are told to drive carefully on the radio. the drivers are told on the radio to drive carefully 7.I almost spent two hours on this exercises. I spent almost two hours on this exercises. 8.Checking carefully,a serious mistake was found in the design. Checking carefully,I found a serious mistake in the design.
M1 U1 一. 把下列短语填入每个句子的空白处（注意所填短语的形式变化）： add up (to) be concerned about go through set down a series of on purpose in order to according to get along with fall in love (with) join in have got to hide away face to face 1 We’ve chatted online for some time but we have never met ___________. 2 It is nearly 11 o’clock yet he is not back. His mother ____________ him. 3 The Lius ___________ hard times before liberation. 4 ____________ get a good mark I worked very hard before the exam. 5 I think the window was broken ___________ by someone. 6 You should ___________ the language points on the blackboard. They are useful. 7 They met at Tom’s party and later on ____________ with each other. 8 You can find ____________ English reading materials in the school library. 9 I am easy to be with and _____________my classmates pretty well. 10 They __________ in a small village so that they might not be found. 11 Which of the following statements is not right ____________ the above passage? 12 It’s getting dark. I ___________ be off now. 13 More than 1,000 workers ___________ the general strike last week. 14 All her earnings _____________ about 3,000 yuan per month. 二.用以下短语造句： 1.go through 2. no longer/ not… any longer 3. on purpose 4. calm… down 5. happen to 6. set down 7. wonder if 三. 翻译： 1.曾经有段时间，我对学习丧失了兴趣。（there was a time when…） 2. 这是我第一次和她交流。（It is/was the first time that …注意时态） 3.他昨天公园里遇到的是他的一个老朋友。（强调句） 4. 他是在知道真相之后才意识到错怪女儿了。（强调句） M 1 U 2 一. 把下列短语填入每个句子的空白处（注意所填短语的形式变化）： play a …role (in) because of come up such as even if play a …part (in) 1 Dujiangyan(都江堰) is still ___________in irrigation(灌溉) today. 2 That question ___________ at yesterday’s meeting. 3 Karl Marx could speak a few foreign languages, _________Russian and English. 4 You must ask for leave first __________ you have something very important. 5 The media _________ major ________ in influencing people’s opinion s. 6 _________ years of hard work she looked like a woman in her fifties. 二.用以下短语造句： 1.make (good/full) use of 2. play a(n) important role in 3. even if 4. believe it or not 5. such as 6. because of