with the preface of Music Notation and Terminology. This is a LibriVox recording. All LibriVox recordings are in the public domain. For more information, or to volunteer, please visit LibriVox.org Recording by Miriam Esther Goldman. Music Notation and Terminology by Carl Wilson Gherkins. The Preface. The study of Music Notation and Terminology by classes in conservatories and in music departments of colleges and normal schools is a comparative innovation. One reason for the non-existence of such courses in the past being the lack of a suitable textbook, in which might be found in related groups clear and accurate definitions of the really essential terms. But with the constantly increasing interest in music study, private and in the public schools, and with the present persistent demand that music teaching shall become more systematic and therefore more efficient in turning out a more intelligent class of pupils, it has become increasingly necessary to establish courses in which the prospective teacher of music, after having had considerable experience with music itself, might acquire a concise and accurate knowledge of a fairly large number of terms, most of which he has probably already encountered as a student, and many of which he knows the general meaning of, but none of which he perhaps knows accurately enough to enable him to impart his knowledge clearly and economically to others. To meet the need of a textbook for this purpose in his own classes, the author has been for several years gathering materials from all available sources. And it is hoped that the arrangement of this material and related groups as here presented will serve to give the student not only some insight into the present meaning of a goodly number of terms, but will also enable him to see more clearly why certain terms have the meaning which at present attaches to them. To this later end, the derivations of many of the terms are given in connection with their definition. The aim has not been to present an exhaustive list, and the selection of terms has, of course, been influenced largely by the author's own individual experience. Hence, many teachers will probably feel that important terms have been omitted that should have been included. For this state of affairs, no apology is offered, except that it would probably be impossible to write a book on this subject which would satisfy everyone in either the selection or actual definition of terms. In formulating the definitions themselves, an attempt has been made to use such words as note, tone, etc., with at least a fair degree of accuracy. And while the attitude of the author on this point may be criticized as being puristic and pedantic, it is nevertheless his opinion that the next generation of music students and teachers will be profited by a more accurate use of certain terms that have been inaccurately used for so long that the present generation has, to a large extent, lost sight of the fact that the use is inaccurate. The author is well aware of the fact that reform is a matter of growth rather than of edict. But he is also of the belief that before reform can actually begin to come, the need of reform must be felt by a fairly large number of actively interested persons. It is precisely because so few musicians realize the need of any change in music terminology that the changes recommended by committees who have given the matter careful thought are so slow in being adopted. It is hoped that some few points at which reform in the terminology of music is necessary may be brought to the attention of a few additional musicians through this volume and that the cause may thus be helped in some slight degree. It is suggested that in using the book for classroom purposes, the teacher emphasized not only the definition and derivation of all terms studied, but the spelling and pronunciation as well. For this latter purpose, a pronouncing index has been appended. It is impossible to give credit to all sources from which ideas have been drawn, but a special mention should be made of the eminently clear and beautifully worded definitions compiled by Professor Waldo S. Pratt or the Century Dictionary and the exceedingly valuable articles on an almost all-inclusive range of topics found in the new edition of Groves Dictionary. A special thanks for valuable suggestions as to the arrangement of the material, etc. are also due to Dr. Raymond H. Stetson, Professor of Psychology, Oberlin College, Arthur E. Hecox, Professor of Theory, Oberlin Conservatory of Music, and Charles I. Rice, Supervisor of Music, Worcester, Massachusetts, as well as to various members of the Music Teacher's National Association who have offered valuable advice along certain specific lines. KWG Oberlin Conservatory of Music, June 1913 End of the Preface Recording by Miriam Esther Goldman 1. The note from Nota, Latin, a mark or sign, consists of either one, two, or three parts, these being referred to respectively as head, stem, and hook. The hook is often called tail or cross-stroke. The stem appears on the right side of the head when turned up, but on the left side when turned down. Begin footnote. It should be noted at the outset that this statement regarding the downturned stem on the left side of the note head and also a number of similar principles here cited refer more specifically to music as it appears on the printed page. In the case of hand-copied music, the downturned stem appears on the right side of the note, thus. Here's a picture of a downturned stem on a note. This is done because of greater facility in writing, and for the same reason other slight modifications of the notation here recommended may sometimes be encountered. In dealing with children, it is best usually to follow as closely as possible the principles according to which printed music is notated in order to avoid those non-satisfying and often embarrassing explanations of differences which will otherwise be unavoidable. End footnote. The hook is always on the right side. Begin footnote. An exception to this rule occurs in the case of notes of unequal values stroked together when the hook appears on the left side, thus. And here's an illustration of notes stroked together with a hook on the left. End footnote. In writing music with pen, the head and hook are best made with a heavy pressure on the pen-point, but in writing at the board they are most easily made by using a piece of chalk about an inch long turned on its side. Two. When only one part or voice is written on the staff, the following rules for turning stems apply. One. If the notehead is below the third line, the stem must turn up. Two. If the notehead is above the third line, the stem must turn down. Three. If the notehead is on the third line, the stem is turned either up or down with due regard to the symmetrical appearance of the measure in which the note occurs. The following examples will illustrate these points. Figure one. Three. When two parts are written on the same staff, the stems of the upper part all turn up, and those of the lower part turn down in order that the parts may be clearly distinguished. Figure two. But in music for piano and other instruments which complete chords can be sounded by one performer and also in simple four part vocal music in which all voices have approximately the same rhythm, several notes often have one stem in common as in figure three. Figure two. Figure three. Four. Notes of small denomination, eighths or smaller, are often written in groups of two or more, all stems in the group being then connected by one cross-stroke. In such a case all the stems must of course be turned the same way, the direction being determined by the position of the majority of note heads in the group. Notes thus stroked may be of the same or of different denomination. See figure four. Figure four. In vocal music notes are never thus stroked when a syllable is given to each note. See page nineteen, section fifty-five. See. Five. Rests, like notes, are best made with a heavy pen-stroke or by using a piece of chalk on its side. See note under section one. The double whole rest, whole rest and half rest occupy the third space unless for the sake of clearness in writing two parts on the same staff they are written higher or lower. The rests of smaller denomination may be placed at any point on the staff, the hooks being always placed on the spaces. The hook of the eighth rest is usually placed on the third space. Rests are sometimes dotted, but are never tied. Six. The G clef should be begun at the second line rather than below the staff. Experiments have shown clearly that beginners learn to make it most easily in this way and the process may be further simplified by dividing it into two parts, thus. Here's an illustration of the curvy line of a G clef next to the vertical straight line. The descending stroke crosses the ascending curve at or near the fourth line. The circular part of the curve occupies approximately the first and second spaces. Seven. The F clef is made either thus illustration of a regular F clef or thus illustration of a more swirly fancy F clef. The dots being placed one on either side of the fourth line of the staff, which is the particular point that the clef marks. The C clef has also two forms, illustration of one type of C clef and illustration of the other type. Eight. The sharp is made with two light vertical strokes and two heavy slanting ones, the slant of the ladder being upward from left to right, illustration of a properly drawn sharp symbol. The sharp should never be made thus, illustration of a regular number symbol. The double sharp is made either thus an X or an asterisk, the first form being at present the more common. Nine. The flat is best made by a downstroke retraced partway up, the curve being made without lifting pen from paper. The double flat consists of two flats. Begin footnote. It is to be hoped that the figure for the double flat suggested by Matheson, who also suggested the St. Andrew's cross for the double sharp, may sometime be re-adopted. This figure was the Greek letter B made thus, it looks like a German S said, and its use would make our notation one degree more uniform than it is at present. End footnote. The natural or cancel is made in two strokes, down right and right down thus, illustration of the components of a natural sign. Ten. The tie usually connects the heads of notes thus, illustration of two notes connected by a tie. Eleven. The dot after a note always appears on a space, whether the note head is on a line or space. See figure five. In the case of a dot after a note on a line, the dot usually appears on the space above that line, if the next note is higher in position and on the space below it, if the following note is lower. Figure five. Note. Correct notation must be made a habit rather than a theory, and in order to form the habit of writing correctly, drill is necessary. This may perhaps be best secured by asking students to write, at the board, or on ruled paper, from verbal dictation thus, teacher says, key of B-flat three-quarter measure, first measure, do a quarter note, re a quarter and me a quarter. Second measure, sol a quarter, la a quarter and sol a quarter. Third measure, la ti do re mi, eighths, strokes in pairs. Fourth measure, high do, a dotted half. Pupils respond by writing the exercise dictated, after which mistakes in the turning of stems, etc., are corrected. The pitch names may be dictated instead of the syllables if desired, and still further practice may be provided by asking that the exercise be transposed to other keys. End of Chapter 1, read by Kara Schellenberg, www.kray.org, on July 31, 2009, in San Diego, California. Chapter 2 of Music Notation and Terminology. This is a LibriVox recording. All LibriVox recordings are in the public domain. For more information or to volunteer, please visit LibriVox.org. Recording by Thovo. Music Notation and Terminology by Carl Wilson Gerkins. Chapter 2, Symbols of Music Defined. 12. A staff is a collection of parallel lines, together with the spaces belonging to them. The modern staff has five lines and six spaces, these being ordinarily referred to as first line, second line, third line, fourth line, and fifth line, beginning with the lowest, and space below, that is, space below the first line, first space, second space, third space, fourth space, and space above. The definition and discussion above refer more specifically to one of the portions of the great staff, the latter term being often applied to the combination of treble and bass staffs with one ledger line between, so commonly used in piano music, etc. 13. The extent of the staff may be increased either above or below by the addition of short lines called ledger lines. Begin footnote. The word ledger is derived from the French word leger, meaning light, and this use of the word refers to the fact that the ledger lines, being added by hand, are lighter, that is, less solid in color than the printed lines of the staff itself. End footnote. And notes may be written on either these lines or on the spaces above and below them. 14. The lines and spaces constituting the staff, including ledger lines, if any, are often referred to as staff degrees, that is, each separate line and space is considered to be a degree of the staff. The tones of a scale are also sometimes referred to as degrees of the scale. 15. A clef. Begin footnote. The word clef is derived from clavus, a key, the reference being to the fact that the clef unlocks or makes clear the meaning of the staff, as a key to a puzzle enables us to solve the puzzle. End footnote. A clef is a sign placed on the staff to designate what pitches are to be represented by its lines and spaces. Thus, for example, the G clef shows us not only that the second line of the staff represents G, but that the first line represents E, the first space F, etc. The F clef similarly shows us that the fifth line of the base staff represents the first A below middle C, the fourth line the first F below middle C, etc. The student should note that these clefs are merely modified forms of the letters G and F, which, among others, were used to designate the pitches represented by certain lines when staff notation was first inaugurated. For a fuller discussion of this matter, see Appendix A, page 101. 16. When the G clef is used, the staff is usually referred to as the treble staff, and when the F clef is used as the base staff, such expressions as singing from the treble clef, or singing in the treble clef, and singing in the treble clef are still frequently heard, but are preferably replaced by singing from the treble staff and singing from the base staff. Fig. 6 shows the permanent names of lines and spaces when the G and F clefs are used. Begin footnote. The Germans use the same pitch designations as we do with two exceptions. That is to say, our B is called them H, and our B flat is called B. The scale of C therefore reads C, D, E, F, G, A, H, C. The scale of F reads F, G, A, B, C, D, E, F. The signatures are in all cases written exactly as we write them. In France and Italy, where the fixed dough system is in vogue, pitches are usually referred to by the syllable names. For example, C is referred to as dough or ut, D as ray, etc. End footnote. 17. The movable C clef. And there's an illustration of a type of C clef or another type of C clef. Formerly in very common use is now utilized for only two purposes, namely one in music written for certain orchestral instruments, cello, viola, etc., of extended range in order to avoid having to use too many ledger lines and two for indicating the tenor part in vocal music. This latter usage seems also to be disappearing, however. And the tenor part is commonly written on the treble staff. It being understood that the tones are to be sung an octave lower than the notes would indicate. The C clef, as used in its various positions, is shown in figures 7, 8, and 9. It will be noted that in each case, the line on which the clef is placed represents middle C. 18. A sharp is a character which causes the degree of the staff with which it is associated to represent a pitch one half step higher than it otherwise would. Thus, in figure 10a, the fifth line and first space represent the pitch F. But in figure 10b, these same staff degrees represent an entirely different tone. F sharp. The student should note that the sharp does not then raise anything. It merely causes a staff degree to represent a higher tone than it otherwise would. There's just as much difference between F and F sharp as between B and C, and yet one would never think of referring to C as B raised. 19. A flat is a character that causes the degree of the staff with which it is associated to represent a tone one half step lower than it otherwise would. See note under section 18 and apply the same discussion here. 20. A double sharp causes the staff degree on which it is placed to represent a pitch one whole step higher than it would without any sharp. Similarly, a double flat causes the staff degree on which it is placed to represent a pitch one whole step lower than it would without any flat. 20. Double sharps and double flats are generally used on staff degrees that have already been sharped or flatted. Therefore, their practical effect is to cause staff degrees to represent pitches respectively a half step higher and a half step lower than would be represented by those same degrees in their diatonic condition. Thus, in figure 10B, the first space in its diatonic condition begin footnote. The expression diatonic condition as here used refers to the staff after the signature has been placed upon it. In other words, after the staff has been prepared to represent the pitches of the diatonic scale. End footnote. Represents F sharp and the double sharp on this degree would cause it to represent a pitch one half step higher than F sharp. That is F double sharp. End of Chapter 2. Recording by Thovo, December 13, 2009. Chapter 3 of Music Notation and Terminology. This is a LibriVox recording. All LibriVox recordings are in the public domain. For more information or to volunteer, please visit LibriVox.org. Music Notation and Terminology by Carl W. Gherkins. Chapter 3. Symbols of Music Defined, continued. 21. The natural begin footnote. It has already been noted, page 6 note, that in the German scale our B-flat is called B and our B is called H. From this difference in terminology has grown up the custom of using H, now made natural sign, to show that any staff degree is in natural condition, i.e. not sharp or flatted. End footnote. Sometimes called cancel, annul the effect of previous sharps, flats, double sharps and double flats within the measure in which it occurs. After a double sharp or double flat, the combination of a natural with a sharp or a natural with a flat is often found. In this case only one sharp or flat is annulled. Sometimes also the single sharp or flat will be found by itself canceling the double sharp or double flat. The natural is often used when a composition changes key, as in figure 11 where a key from E to G is shown. 22. The group of sharps or flats, or absence of them at the beginning of a staff partially indicates the key in which the composition is written. They are called collectively the key signature. 23. The same key signature may stand for either one of two keys, the major key or its relative minor. Hence in order to determine in what key a melody is in, one must note whether the tones are grouped around the major tonic dough or the minor tonic law. In a harmonized composition it is almost always possible to determine the key by referring to the last base note. If the final chord is clearly the dough chord the composition is in the major key. But, if this final chord is clearly the law chord then it is almost certain that the entire composition is in the minor key. Thus, if a final chord appears as that in figure 12 the composition is clearly in G major. While if it appears as in figure 13 it is just as surely in E minor. 24. Sharps, flats, naturals, double flats and double flats occurring in the course of the composition, i.e. after the key signature are called accidentals. Whether they actually cause a staff degree to represent a different pitch as in figure 14 or simply make clear a notation about which there might otherwise be some doubt as in figure 15 measure 2. The effect of such accidentals terminates at the bar. 25. In the case of a tie across a bar, an accidental remains in force until the combined value of the tied notes expires. In figure 16, first measure third beat, an accidental sharp makes the third space represent the pitch C sharp. By virtue of the tie across the bar the third space continues to represent C sharp through the first beat of the second measure. But for the remainder of the measure the third space will represent C unless the sharp is repeated as in figure 17. 26. The following rules for making staff degrees represent pitches different from those of the diatonic scale will be found to be useful by the beginner in the study of musical notation. These rules are quoted from the Warchester musical manual by Charles I. Rice. 1. To sharp a natural degree use a sharp. 2. To sharp a sharp degree use a double sharp. 3. To sharp a flat a degree use a natural. 4. To flat a natural degree use a flat. 5. To flat a flat a degree use a double flat. 6. To flat a sharp degree use a natural. 23. 27. When two different notations represent the same pitch the word and harmonic is applied. Thus we may say that F sharp and G flat on keyboard instruments at least are harmonically the same. The word and harmonic is used in such expressions as and harmonic change and harmonic keys and harmonic interval and harmonic modulation and harmonic relation etc. and in all such combinations it has the same meaning that is a change in notation but no change in the pitch represented. 28. A note is a character expressing relative duration which, when placed on a staff indicates that a certain tone is to be sounded for a certain relative length of time. The pitch of the tone to be sounded is shown by the position of the note on the staff while the length of the time it is to be prolonged is shown by the shape of the note. Thus, example a half note on the second line of the treble staff indicates that a specific pitch G is to be played or sung, her period of time twice as long as would be indicated by a quarter note in the same composition. 29. A rest is a character which indicates a rhythmic silence of a certain relative length. 30. The notes and rests in common use are as follows whole note an open note head without stem half note an open note head with stem quarter note a closed note head with stem in one hook sixteenth note a closed note head with stem in two hooks thirty-second note a closed note head with stem in three hooks whole rest half rest quarter rest sixteenth rest thirty-second rest 31. The English names for these notes are whole note semi-brave quarter note eighth note sixteenth note thirty-second note the corresponding rests are referred to by the same system of nomenclature example semi-brave rest 32. 64 and 120 eighth notes are occasionally found but are not in common use. The double whole note made or another picture of a double whole note is still used especially in English music which frequently employs the half note as a beat unit. Thus in four half measures the brevet would be necessary to indicate a tone having four beats. 33. The whole rest has a peculiarity of usage not common to any other duration symbol that is it is often employed as a measure rest feeling an entire measure of beats no matter what the measure signature may be. Thus not only in four quarter measures but in two quarter, three quarter six eighths and other varieties the whole rest feels the entire measure having a value sometimes greater sometimes less than the corresponding whole note. Because of this peculiarity of usage the whole rest is termed taktpasa measure rest by the Germans. 34. A bar is a vertical line across the staff dividing it into measures. The word bar is often used cinemously with measure by orchestral conductors and others thus being at the fourteenth bar after J. This use of the word although popular is incorrect. 35. A double bar consists of two vertical lines across the staff at least one of the two being a heavy line. The double bar marks the end of a division movement or entire composition. End of chapter three. Chapter four of music notation and terminology. This is a LibriVox recording. All LibriVox recordings are in the public domain. For more information or to volunteer please visit LibriVox.org Recording by Jennifer Stearns Music notation and terminology by Carl Wilson Kirkens Chapter four abbreviations, signs, etc. 36. A double bar or single heavy bar with either two or four dots indicates that a section is to be repeated. If the repeat marks occur at only one point the entire proceeding part is to be repeated. But if the marks occur twice, the first time at the right of the bar, with the second time at the left only the section thus enclosed by the marks is to be repeated. 37. Sometimes a different cadence or ending is to be used for the repetition and this is indicated as in Figure 24. 38. The Italian word base is occasionally used to indicate that a certain passage or section is to be repeated. This use is becoming obsolete. 39. The words da cappo dc mean literally from the head. Namely repeat from the beginning. The words da signo indicate a repetition from the sign. S with squiggly line instead of from the beginning. In the case of both dc and ds, the word fine meaning literally the end is ordinarily used to designate the point at which the repeated section is to terminate. The fermata was formally in common use for the same purpose. But it seldom so employed at present. dc footnote The word sign is a contraction of the Italian word sino meaning as far as or until in the term given above. It is really superfluous as the word al includes in itself both preposition and article meaning to the end footnote. al fine means repeat from the beginning to the word fine. dc al fermata means repeat to the fermata or hold. dc senza repitizione or dc massenza repitizione both mean repeat from the beginning but without observing other repeat marks during the repetition. dc ipua la coda means repeat the first section only to the mark circle with a cross through it then skip to the coda. dc l 40 In certain cases where the repetition of characteristic figures can be indicated without causing confusion it is the practice of composers especially in orchestral music to make use of certain signs of repetition. Some of the commonest of this abbreviation are shown in the following examples. In figure 28 the repetition of an entire measure is called for. The word simile sometimes segue indicates that a certain effect previously begun is to be continued as for example staccato playing pedaling, style of bowing and violin music etc. The word segue is also occasionally used to show that an accompaniment figure especially in orchestral music is to be continued. 42 When some part is to rest for two or more measures several methods of notation are possible. A rest of two measures is usually indicated thus a bar over the third line three measures thus two bars over the third line with three above four measures thus a bar over the second and third space or the four above. Rest of more than four measures are usually indicated in one of the following ways lines throughout the middle of the staff with the number of rest above sometimes the number of measures is written directly on the staff thus number right in the staff. 43 The letters gp general pause or grossé pause the words lunga pausa or simply the word lunga are sometimes written over a rest to show that there is to be a prolonged pause or rest in all parts such expressions are found only in unsolvable music namely music in which several performers engage at the same time. 44 the fermata or hold in arch of the da under it over a note or chord indicates that the tone is to be prolonged the duration of the prolongation depending upon the character of the music and the taste of the performer or conductor it has already been noted that the hold over a bar was formally used to designate the end of the composition as the word finé is employed at presence but this usage has practically disappeared and the hold over the bar now usually indicates a short rest between two sections of a composition 45 the sign 8va an abbreviation of al octava literally at the octave above the staff indicates that all tones are to be sounded an octave higher than the notes would indicate. When found below the staff the same sign serves to indicate that the tones are to be sounded an octave lower the term 8va basa has also the slaughter of signification 43 sometimes the word loco in place is used to show that the part is no longer to be sounded an octave higher or lower but this is more often indicated by the termination of the dotted or wavy line 47 the sign col 8 col octava with the octave shows that the tones an octave higher are to be sounded with the tones indicated by the printed notes 48 for the sake of definiteness in referring to pitches a particular name is applied to each octave and all pitches in the octave are referred to by means of a uniform nomenclature the following figure will make the system clear thus for example great g written simply g is a g represented by the first line of the base staff small a written lowercase a is represented by the fifth line of the base staff two line g is represented by the space above the fifth line treble staff three line c written c with three lines above it is represented by the second added line above the treble staff etc the one lined octave may be described as the octave from middle c to the b represented by the third line of the treble staff the one within that octave is referred to as one lined thus one lined d, one lined g etc the scientific works on acoustics etc the features in the sub-optive or sub-contra-optive as it is often called are referred to as c subscript 2 d subscript 2 e subscript 2 etc those in the contra-optive as c subscript 1 d subscript 1 etc in the great octave as c superscript 1 d subscript 1 etc in the small octave as c superscript 2 d subscript 2 etc end of chapter 4 recording by Jennifer Stearns Concord, New Hampshire chapter 5 of music notation and terminology this is a LibriVox recording all LibriVox recordings are in the public domain for more information or to volunteer visit LibriVox.org music notation and terminology by Carl Wilson Gerkins read and recorded by Sandra chapter 5 abbreviations signs etc continued 49 a dot after a note shows that the value of the note is to be half again as great as it would be without the dot the value is to be three halves that of the original note 50 when two dots follow the note the second dot adds half as much as the first dot has added i.e. the entire value is seven fourths that of the original note 51 when three dots follow the note the third dot adds one half the value added by the second i.e. the entire value of the triple dotted note is 15 eighths that of the original note 52 a dot over or under a note is called the staccato mark and indicates that the tone is to be sounded and then instantly released in music for organ or some other instruments the staccato note is sometimes interpreted differently this depending on the character of the instrument on stringed instruments of the violin family the staccato effect is usually secured by a long rapid stroke of the bow for each tone in the case of harp and drum the hand is quickly brought into contact with the vibrating thus stopping the tone instantly on the organ the tone is often prolonged to one half the value of the printed note before the keys are released 53 the wedge shaped dash over the note staccatissimo was formerly employed to indicate a tone still more detached than that indicated by the dot but this sign is really superfluous and is seldom used at present 54 a tie is a curved line connecting the heads of two notes that call for the same tone it indicates that they are to be sounded as one tone having a duration equal to the combination value of both notes e.g a half note tied to a quarter note would indicate a tone equal in duration length to that shown by a dotted half note two half notes tied would indicate a tone equal in duration to that shown by a whole note see examples under sections 49, 50 and 51 figure 30 illustrates the more common variety of tie well figure 31 shows an example of the enharmonic tie footnote 10 for definition of enharmonic see page 10 section 27 55 the slur is used in so many different ways that it is impossible to give a general definition it consists of a curved line sometimes very short in which case it looks like the tie but sometimes very long connecting 10, 15 or more notes some of the more common uses of the slur are a to indicate a legato sustained or connecting tones as contrasted with staccato detached ones in violin music this implies playing all tones thus slurred in one bow in music for the voice and for wind instruments it implies singing or playing them in one breath B as a phrase mark in the interpretation of which the first tone of the phrase is often accented slightly and the last one shortened in the value this interpretation of the phrase is especially common when the phrase is short as in the two note phrase and when the tones constituting the phrase are quite short duration e.g. the phrase given in figure 32 would be played approximately as written in figure 33 but if the notes are of greater value especially in slow tempo the slur merely indicates legato i.e. sustained or connected rendition figure 34 illustrates such a case this is a matter of such diverse usage that it is difficult to generalise regarding it the tendency seems at present to be in the direction of using the slur in instrumental music and in rock exclusively it being understood that unless there is some direction to the contrary the tones are to be performed in a connected manner C in vocal music to show that two or more tones are to be sung to one syllable of text see figure 35 figure 35 Mendelssohn St. Paul remember his children in notes of small denomination eighths or smaller the same thing is often indicated by stroking the stems together as in figure 36 ever and ever and ever and this can only be done in cases where the natural grouping of notes in the measure will not be destroyed D to mark the special note groups triplets etc in which case the slur is accompanied by a figure indicating the number of notes in the group C figure 37a A the most common of these irregular note groups is the triplet which consists of three notes to be performed in the time ordinarily given two of the same value sometimes the triplet consists of only two notes as in figure 37b B B in such a case the first two of the three notes composing the triplet are considered to be tied when the triplet form is perfectly obvious the figure 3 as well as the slur may be omitted other examples of irregular note groups together with the names commonly applied follow 56 the combination of slur or tie and dots over the notes indicates the tones are to be somewhat detached but not sharply so this effect is sometimes erroneously termed portamento, lit, carrying but this term is more properly reserved for an entirely different effect this when a singer or player on a string instrument passes from one high tone to a low one or vice versa touching likely on some or all of the diatonic tones between the two melody tones 57 the horizontal dash over a note indicates that the tone is to be slightly accented and sustained this mark is also sometimes used after a staccato passage to show that the tones are no longer to be performed in detached fashion but are to be sustained this latter use especially common in music for stringed instruments 58 the combination of dash and dot over a note indicates that the tone is to be slightly accented and separated from its neighbouring tones 59 accent marks are made in a variety of fashions the most common forms follow horizontal accent symbol vertical accent symbol SF FZ all indicate that a certain tone or chord is to be differentiated from its neighbouring tones or chords by receiving a certain relative amount of stress 60 in music for keyboard instruments it is sometimes necessary to indicate that a certain part is to be played by a certain hand the abbreviations are H right hand MD mano destra Italian and MD ma droite French designate that a passage or tone is to be played with the right hand while LH left hand MS Italian and MG man gauche French show that the left hand is to be employed 61 the wavy line placed vertically beside a chord indicates that the tones are to be sounded consecutively instead of simultaneously beginning with the lowest tone all tones being sustained until the duration value of the chord has expired this is called arpeggio playing when the wavy line extends through the entire chord covering both staffs as in figure 38 all the tones of the chord are to be played one after another beginning with the lowest but if there is a separate wavy line for each staff as at figure 39 then the lowest tone represented on the upper staff is to be played simultaneously with the lowest tone represented on the base staff the word arpeggio plural arpeggi is a derivation of the Italian word arpa meaning harp and from this word arpa and its corresponding verb arpeggiare to play on the harp are derived also a number of other terms commonly used in instrumental music among these are arpeggiamento, arpeggiando arpeggiato etc all of these terms referring to a harp style of performance the tones being sounded one after another in rapid succession instead of simultaneously as on the piano 62 the sign crescendo the crescendo symbol over a note indicates that the tone is to be begun softly gradually increased in power and as gradually decreased again ending as softly as it began in vocal music this effect is called messa di voce 63 in music for stringed instruments of the violin family the sign down bow symbol like an upside down V indicates down bow and the sign up bow symbol like a V indicates up bow in cello music the down bow sign is sometimes written cello down bow symbol like two vertical lines with a thick horizontal line joining them at the top end of chapter 5 chapter 6 of music notation and terminology this is LibriVox recording all LibriVox recordings are in the public domain for more information or to volunteer please visit LibriVox.org recording by Jennifer Stearns music notation and terminology by Carl Wilson Gerkins chapter 6 embellishments 64 embellishments or graces French Agremont our ornamental tones either represented in full in the score or indicated by certain signs the following are the embellishments most commonly found trill or shake mordant inverted mordant or prowl trill turn apagiatora and axiocatora usage varies greatly in the interpretation of the signs representing these embellishments and it is impossible to give examples of all the different forms the following definitions represent therefore only the most commonly found examples and the most generally accepted interpretations 65 the trill or shake consists of the rapid alternation of two tones to the full value of the printed note the lower of these two tones is represented by the printed note while the upper one is the next higher tone in the diatonic scale of the key in which the composition is written the interval between the two tones may therefore be either a half step or a whole step whether the trill is to begin with the principal tone represented by the printed note above is a matter of some dispute among theorist and performers but it may safely be said that the majority of modern writers on the subject would have it begun on the principal tone rather than on the tone above figure 40 when the principal tone is preceded by a small note on the degree above it is of course understood that the trill begins on the tone above figure 41 the trill is indicated by the sign tr the above examples will be termed perfect trills because they close with the turn by inference an imperfect trill is one closing without a turn 66 the mordant consists of three tones first the one represented by the printed note second the one next below it in the diatonic scale third the one represented by the printed note again figure 42 67 the double or long mordant has five tones sometimes seven instead of three the first two of the three tones of the regular mordant being repeated once or more see figure 43 in the case of both mordant and double mordant the tones are sounded as quickly as possible the time taken by the embellishment being subtracted from the value of the principal note is printed 68 the inverted mordant note the absence of the vertical line is like the mordant except of the tone below is replaced by the tone above in each case this ornament is sometimes called a transient shake because it is really only a part of the more elaborate grace called trill see figure 44 the confusion at present attending the interpretation of the last two embellishments described might be largely obviated in a recent writer begin footnote elson dictionary of music article mordant and footnote to call the one the upward mordant and the other the downward mordant were to be universally adopted 69 the term consists of four tones first the diatonic scale tone above the principal tone second the principal tone itself third the tone below the principal tone and fourth the principal tone again when the sign occurs over a note of small value in rapid tempo figure 45 the term consists of four tones have equal value but if it occurs over a note of greater value or in a slow tempo the tones are usually played quickly like the mordant and the fourth tone is then held until the time value of the note has expired figure 46 70 when the turn sign is placed a little to the right of the note the principal tone is sounded first and held to almost its full time value then the turn is played just before the next tone of the melody in this case the four tones are of equal length as in the first example see figure 47 the student should note the difference between these two effects in the case of a turn over the note the turn comes at the beginning but in the case of the sign after the note the turn comes at the very end but in both cases the time taken by the embellishment is taken from the time value of the principal note for further details see groves dictionary music and musicians volume 5 page 184 also elson opus satanum page 274 71 sometimes an accidental occurs with the turn and in this case when written above the sign it refers to the highest tone of the turn but when written below to the lowest figure 48 72 in the inverted turn the order of tones is reversed the lowest one coming first the principal tone next the highest tone third last figure 49 73 the apogiatura lit leaning note consists of ornamental tone introduced before a tone of a melody thus delaying the melody tone until the ornamental tone has been heard the time taken of this ornamental tone is taken from that of the melody tone the apogiatura was formally classified into long apogiatura and short apogiatura but modern writers seem to consider that the term short apogiatura to be synonymous with apogiatura begin footnote in organ music the apogiatura is still taken to mean that the embellishing tone and the melody tone are to be sounded together the former being then instantly released while the latter is held to its full time value end footnote and to avoid confusion the word acicator will be used in this sense and defined under its own heading 74 three rules for the interpretation of the apogiatura are commonly cited namely 1. when it is possible to divide the principal tone into halves then the apogiatura receives one half the value of the printed note figure 50 2. when the principal note is dotted division into halves being therefore not possible the apogiatura receives two thirds of the value figure 51 3. when the principal note is tied to a note of smaller denomination the apogiatura receives the value of the first of the two notes figure 52 75 the acicator or short apogiatura is written like the apogiatura except that it has a light stroke across its stem it has no definite duration value but is sounded as quickly as possible taking its time from that of the principal tone the apogiatura is always accented but the acicator never is the stress always falling on the melody tone C. grove opus citatum volume 1 page 96 the use of embellishments is on the wane and the student of today needs the above information only to aid him in the interpretation of music written in previous centuries in the early days of instrumental music it was necessary to introduce graces of all sorts because the instruments in use were not capable of sustaining tone for any length of time but with the advent of the modern piano with its comparatively great sustaining power with the advent and vocal music of a new style of singing German leader singing as contrasted with Italian Chlorosaurus singing ornamental tones were used less and less and when found now are usually written out in full in the score instead of being indicated by science End of Chapter 6 Recording by Jennifer Stearns Concord, New Hampshire Chapter 7 This is a LibriVox recording All LibriVox recordings are in the public domain For more information or to volunteer, please visit LibriVox.org Recording by Gillian Brandt St. Paul, Minnesota Music Notation and Terminology by Carl Wilson Gherkins Chapter 7 Scales 76 A scale from Scala a Latin word meaning ladder or German tone lighter is an ascending or descending series of tones progressing according to some definite system and all bearing in the case of tonality scales at least a very intimate relation to the first note the key tone or tonic see page 28 section 78 also note 1 at bottom of page 38 Many different kinds of scales have existed in various musical eras the point of resemblance among them all being the fact that they have all more or less recognized the octave as the natural limit of the series the difference among the various scales has been in the selection of intervals between the scale tones and consequently in the number of tones within the octave thus e.g. in our musical scale intervals between the tones are all whole steps except 2 which are half steps and the result is a scale of 8 tones including in this number both the key tone and its octave but in the so called pentatonic scale of the Chinese and other civilizations we find larger intervals e.g. the step and a half and consequently a smaller number of tones within the octave thus in the scale upon which many of the older scotch folk songs are based the intervals are arranged as follows 1 whole step 2 whole step 3 step and a half 4 whole step 5 step and a half the result is a scale of 6 tones corresponding approximately with c, d, e, g, a, c in our modern system the term pentatonic is thus seen to be a misnomer since the 6th tone is necessary for the completion of the series just as the 8th tone is essential in our diatonic scales the following Chinese tune called jasmine is based on the pentatonic scale 77 in setting the theory of the scale the student should bear in mind the fact that a scale is not an arbitrary series of tones which someone has invented and which others are required to make use of it is rather the result of a customing the ear to certain melodic combinations that were originally hit upon by accident and finally analyzing and systematizing these combinations into a certain definite order or arrangement the application of this idea may be verified when it is recalled that most primitive peoples have invented melodies of some sort but that only in modern times and particularly since the development of instrumental music have these melodies been analyzed and the scale upon which they are referred the inventors of the melodies being themselves wholly ignorant of the existence of such scales 78 a key is a number of tones grouping themselves naturally both melodically and harmonically about a central tone the key tone the word tonality is often used synonymously with key in this sense the difference between key and scale that while both key and scale employ the same tone material by key we mean the material in general without any particular order or arrangement in mind while by scale we mean the same tones but now arranged into regular ascending or descending series it should be noted in this connection also that not all scales present an equally good opportunity of having their tones used as a basis for tonality or key feeling neither the chromatic nor the holst up scale possess the necessary characteristics for being used as tonality scales in the same sense that our major and minor scales are used 79 there are three general classes of scales extent at the present time one diatonic two chromatic three whole tone 80 the word diatonic means through the tones in other words through the tones of the key and is applied to both major and minor scales of our minor tonality system in general a diatonic scale may be defined as one which proceeds by half steps and whole steps attached into this principle in the progression 6 to 7 in the harmonic minor scale which is of course a step and a half 81 a major diatonic scale is one in which the intervals between the tones are arranged as follows one whole step two whole step three half step five whole step six whole step seven half step eight in other words a major diatonic scale is one in which the intervals between three and four and between seven and eight are half steps all the others being whole steps a composition based on this scale is said to be written in the major mode or in a major key a diatonic scale may begin on any of the twelve pitches C C sharp or D flat D D sharp or E flat E F F sharp or G flat G G sharp or A flat A A sharp or B flat B but in each case it is the same scale because the intervals between its tones are the same have one major scale only but this scale may be written in many different positions and may be sung or played beginning on any one of a number of different pitches 82 it is interesting to note that the major scale consists of two identical series of four tones each i.e. the first four tones of the scale are separated from one another by exactly the same intervals and these intervals appear in exactly the same order as in the case of the last four tones of the scale figure 53 will make this clear the first four tones of any diatonic scale major or minor are often referred to as the lower tetrachord and the upper four tones is the upper tetrachord it is interesting further to note that the upper tetrachord of any sharp scale is always used without change as the lower tetrachord of the next major scale involving sharps while the lower tetrachord of any flat scale is used as the upper tetrachord of the next flat scale see figures 54 and 55 in figure 54 the first four notes you hear compose upper tetrachord from scale of C the second four notes you hear compose new tetrachord to complete scale of G in figure 55 the first four notes you hear compose the lower tetrachord from scale of C and the final four notes you hear compose new tetrachord to complete scale of F 83 from the standpoint of notation the major scale may be written in 15 different positions as follows scale number one C major no sharps or flats scale number two G major one sharp F scale number three D major two sharps F and C scale number four A major scale number five E major four sharps F C G and D scale number six B major five sharps F C G D and A scale number seven F sharp major six sharps F C G D A and E scale number eight C sharp major seven sharps F C G D A E B scale number nine F major one flat B scale number ten B flat major two flats B and E scale number eleven E flat major three flats B E and A scale number twelve A flat major four flats B E A and D scale number thirteen D flat major five flats B E A D and G scale number fourteen G flat major six flats B E A D G and C scale number fifteen C flat major seven flats B E A D G C and F it will be observed that in the above series of scales those beginning on F sharp and G flat call for the same keys on the piano i.e. while the notation is different the actual tones of the scale are the same the scales of C sharp and D flat likewise employ the same tones when two scales thus employ the same tones but differ in notation they are said to be and harmonic cf page thirty eight section ninety three note the student is advised to adopt some uniform method of writing scales preferably the one followed in those given above the necessary sharps and flats appearing before the notes in the scales and then repeated collectively at the end as a signature he is also advised to repeat these scales and signatures over and over until absolute familiarity is attained E G E F sharp G sharp A B C sharp D sharp E signature for sharps F C G and D end of chapter seven recording by Gillian Brandt Saint Paul Minnesota chapter eight of music notation and terminology this is a LibriVox recording all LibriVox recordings are in the public domain for more information or to volunteer please visit LibriVox.org music notation and terminology by Carl W. Gerkins chapter eight notes continued 84 the minor diatonic scale is used in several slightly different forms but the characteristic interval between the first and third tones which differentiates it from the major scale remains the very same in every case this interval between the first and third notes consists of four half steps in the major scale and of three half steps in the minor scale and this difference in size has given rise to the designation major for the scale having the larger third or minor for the scale having the smaller one 85 the original or primitive form of the minor scale has its tones arranged as follows one whole step two half step three whole step four half step five half step six whole step seven whole step as its name implies this is the oldest of the three forms being derived from the old Greek Aeolian scale but because of the absence of a leading tone it is suitable for the simplest one park music only and is therefore a little used at present 86 the harmonic minor scale is like the primitive form except that it substitutes a tone one half step higher for the seventh tone of the older i.e. the primitive form this change was made because the development of writing music in several parts particularly harmonic part writing made necessary a leading tone i.e. a tone with a strong tendency to move on up the key tone as a closing point in order to secure a tone with such a strongly upward tendency the interval between seven and eight had to be reduced in size to a half step it should be noted that this change in the seventh note of the scale caused an interval of a step and a half between the six and seventh tones of the scale one whole step half step three whole step four whole step five half step six step and a half seven half step 87 the melodic minor scale substitutes a tone one half step higher than six as well as one and a half step higher than seven but this change is made in the ascending scale only in the primitive form the higher sixth commonly referred to as the raised six was used to get rid of the unmelodic interval of a step and a half begin footnote the step and a half argument in second is unmelodic because it is the same size as a minor third and the mind finds it difficult to take it as a second note representing it being on adjacent staff degrees an interval of the same size as a third and footnote argument in second while the return of the primitive form in descending is made because the ascending form is too much like the major tonic scale one whole step two half step three whole step four whole step five whole step six whole step seven half step seven whole step six half step five whole step four whole step three half step two whole step this form is used only to a very limited extent and then principally in vocal music the harmonic form being in almost universal use in spite of the argument in second the minor scale in its various positions up to five sharps and five flats and in all three forms follows a composition based on any one of these forms or upon a mixture of them which often occurs is said to be in the minor mode it will be noted that the first four tunes are alike in all three forms i.e. the lower tetra chord in the minor scale is invariable no matter what may happen to the upper tetra chord the sine plus marks the step and a half note the student is advised to recite the harmonic form of the minor scales was suggested in the case of the major scale noting that the raised seventh does not affect the key signature example e f sharp g a b c d sharp e signature one sharp f eight nine a minor scale having the same signature as a major scale is said to be its relative minor example e is the relative major of g c of e flat d of f etc the smaller letter being used to refer to the minor key or scale well the capital letter indicates a minor scale unless accompanied by the word minor relative keys are therefore defined as those having the same signature g and e are relative keys as are also a and f sharp etc 90 a minor scale being with the same tone as a major scale is referred to as its tonic minor thus c with three flats in its signature tonic minor of c with all degrees in natural condition e with one sharp is the tonic minor of e with four sharps etc tonic keys are therefore those having the same key tone the eight tones of the diatonic scale both major and minor are often referred to by specific names as follows one tonic the tone is the principal tone or generating tone of the key i.e. it is the tone two super tonic above the tone three midway between tonic and dominant four subdominant the underdominant this name does not refer to the position of the tone under the dominant but the fact that the fifth below the tonic is also a dominant tone just as the fifth above is the upper dominant dominant the governing tone from the latin word dominus meaning master super dominant above the dominant or submediant midway between tonic and subdominant leading tone the tone which demands resolution of the tonic or half step above it octave the eighth tone 92 the syllables commonly applied to the various major and minor scales in teaching sight singing are as follows be in footnote these syllables are said to have been derived originally from the initial syllables of the hymn to saint john the music of which was a typical Gregorian chant the application of these syllables to the scale tones will be made clear by reference to the hymn as given below it will be observed that the hymn provided syllables only for the six tones of the hexachord then recognized when the octave scale was adopted early in the sixteenth century the initial letters of the last line s and i were combined into a syllable for the seventh tone and footnote major do re mi fa sol la minor original la ti do re mi fa sol la harmonic la ti do re mi fa si la melodic la ti do re mi fi si la sol fa mi re do ti la it is interesting to study the changes in both spelling and pronunciation that have occurred and are still occurring in the syllables the first one was changed to do as early as the sixteenth century because of the difficulty of pronouncing a good tone on for the same reason and also in order to avoid having two diatonic syllables with the same initial letter the tonic sol fa system invented in England about 1812 and systemized about 1850 changed c to t and this change has been almost universally adopted by teachers of sight singing in this country the more elaborate tonic sol fa spelling of the diatonic symbols do la etc has not however been favorably received in this country and the tendency seems to be towards still further simplification rather than towards elaboration it is probable that further changes in both spelling and pronunciation will be made in the near future one such change that seems especially desirable being some other syllable for re for the second tone of the major scale so that the present syllable may be reserved for flat 2 thus providing a uniform vowel sound for all intermediate tones of the descending chromatic scale as is already the case in the ascending form 93 the chromatic scale begin footnote the student should differentiate between the so called tonality scales like the major and minor the tones of which are actually used as a basis for key feeling with the familiar experience of coming home to the tone after a melodic or harmonic excursion and on the other hand the purely artificial and mechanical construction of the chromatic scale and footnote is one which proceeds always by half steps its intervals are therefore always equal no matter with what tone it begins since however we have from the standpoint of the piano keyboard five pairs of tones begin footnote most other and harmic notations are possible although the five pairs of tones above referred to are the most common thus E sharp and F harmonically the same also C flat and B C sharp and B double sharp etc and footnote which are and harmonically the same it may be readily seen that the chromatic scale might be notated in all sorts of fashions and this is in fact the real status of the matter there being no one method uniformly agreed upon by composers Perry dictionary article chromatic recommends writing the scale with such accidentals this can occur in chromatic chords without changing the key in which the passage occurs thus taking C as a type the first accidental will be D flat as the upper note of the minor ninth on the tonic next will be E flat the minor third of the key the next F sharp the major third of the super tonic occur without causing modulation and the remaining two will be A flat and B flat the minor sixth and seventh of the key according to this plan the chromatic scale beginning with C would be spelled C D flat D E flat E F F sharp G A flat A B flat B C the form being the same both descending and descending this is of course written exclusively from a harmonic standpoint and the advantage of such a form is its definiteness 94 for sight singing purposes the chromatic scale begin footnote the word chromatic means literally colored and was first applied to the intermediate tones because by using them the singer could get smoother and more i.e. could get more color than by using only the diatonic tones composers were not long discovering the peculiar value of these additional tones and soon found that these same tones were exceedingly valuable also in modulating hence the two uses of intermediate tones at the present time first to establish a melody second to modulate to another key and footnote is usually written by representing the intermediate tones in ascending by sharps in some cases naturals and double sharps and intermediate tones and then descending by flats sometimes naturals and double flats this chromatic scale in nine different positions written from this standpoint follows and the syllables most commonly applied in sight singing have also been added in the first two scales and many is asked to note that because of the very common practice of modulating to the dominant and subdominant keys the intermediate tones sharp 4 and flat 7 are quite universally used in both ascending and descending melody patterns in other words the scale that follow would be more nearly represented actual usage if in each case sharp 4 phi were substituted for flat 5 in the descending scale and a flat 7 t were substituted for the sharp 6 li in the ascending form note in writing chromatic scales from the sight singing standpoint the student is urged to adopt a 3 step process first writing the major diatonic scale both ascending and descending second marking the second steps third inserting accidental notes calling for the intermediate tones in the above chromatic scales these intermediate tones have been represented by black note heads so as to differentiate them from the notes representing diatonic scale tones 95 the whole step scale the third type mentioned in section 79 is as its name implies a scale in which the interval between the tones consists in every instance of whole steps this reduces the number of tones in the scales to 7 beginning with C the scale reads C D E F sharp or G flat A flat B flat C this scale has been used somewhat extensively by the ultra modern french school of composition represented by Debussy, Ravel and others but it is not making any progress towards universal adoption the remarks of a recent english writer begin footnote stanford musical composition 1911 page 17 and footnote on the subject may be interesting to the student who is puzzled by the apparent present day tendencies of french music he says the student of some interesting modern developments will also speedily discover that the adoption of the so called whole tone scale as a basis of music is except upon a keyed instrument tuned to the compromise of equal temperament unnatural and impossible no player upon a stringed instrument can play the scale of whole tones and arrive at an octave which is in tune with the starting note unless he deliberately changes one of the notes on the road and alters it while playing it the obvious result of the application of the whole tone scale to an orchestra or a string quartet would be to force them to adopt the equal temperament of the piano forte and play every interval except the octave out of tune when this modification had taken hold all music in the pure scale would be distorted and destroyed unless string players were to phase the practically impossible drudgery of studying both the equal temperament and the pure scale from the start and were able to tackle either form at a moment's notice and thorough knowledge of the natural genesis of the scale of western nations will be the best antidote to fads founded upon ignorance of it it is a curious commentary upon this question that wanger in the opening of the third act of Tristan bars 6 to 10 experimented with the whole tone scale and drew his pen through it as it was to be expected from a composer whose every work proves the writer to have had the pure scale inbred in him the difference of opinion among acousticians as to whether Mr. Stanford is correct in his scientific assumptions regarding the difference between tempered and pure scales begin footnote recent tests in Germany seem to prove conclusively that the tempered scale is the scale ordinarily employed by both vocalists and players on stringed instruments and that the ideal of an agitation for a pure i.e. untempered scale and vocal stringed instrument is somewhat a myth end footnote but even so there is a far more potent reason why the whole step scale will probably never become as popular as the major and minor scales are now that is the fact that it offers no possibility of in calculating tonality feeling which has always been the basis of the simplest primitive music tonality scales give rise to a feeling of alternate periods of contraction and relaxation in active tone or chord followed by a passive one but no such effect as possible in the whole step scale and it seems suitable therefore only for the class of music whose outlines are purposefully intended to be vague and indefinite the impressionistic style of music writing end of chapter 8 chapter 9 music notation and terminology Carl W. Gherkins this is a LibriVox recording all LibriVox recordings are in the public domain for more information or to volunteer please visit LibriVox.org recording by Jeffrey Powers of the Geek-Azine podcasts chapter 9 auxiliary words and endings number 96 being a list of articles adverbs, conjunctions prepositions and endings often utilized in compounding terms relating to musical effects ah a preposition fiercely translated to at four by in with towards acapella in church style a capriccio at the fancy of the performer adu men's for two hands a mesa voce with half voice a la or a la in the manner of a la marcia in the style of a march a sai very or very much alegro a sai very fast ben well ben marcato well marked coi can cola colé coló with or with the can amore with tenderness cola voce with the voice come as like comprimo as at first contra against in compound words it means an octave below da from da capo from the head di with of for di bravura with daring di morto exceedingly very much alegro di morto exceedingly rapid dapio double dapio movimento double movement ed et and cresce excel or crescent and accelerando louder and faster ensemble ensemble together the opposite of solo il la le le di il beso the base listesso tempo the same speed the same speed il più the most il più forte passable as loudly as possibleissimo Italian superlative ending forte fortissimo ino etto Italian diminutive endings andante andantino poco pocchetto meno less meno forte that's loud mente the ending which changes a noun or adjective to an adverb largo largamente mezzo or mezza half or medium mezzo forte medium loud molto much or very much molto crescent very much louder nel nella et cetera in the or at the nel batter at the downbeat non not non tanto not too much osia or else osia più the sale or else more easily per or per il volino for the violin più peu spelling little un più crescent a little increase in tone più I accent you more più forte more loudly poco little poco a poco little by little poi then poi la coda and then the coda passable possible as loudly as possible as loudly as possible quasi in the manner of allegro quasi andante in the manner of allegro quasi andante a fairly rapid movement yet in the style of an andante almost as slow as an andante sans without sans pedales without pedals sempe always or continually sempe forte a long passage to be played forte throughout its entirety senza without senza accompanimento without accompaniment sinon sin as far as see page 14 note on formata which was formally in common use for the same purpose but is seldom so employed at present solo alone, opposite of ensemble sub under or lower subdominant the under dominant tanto same as troppo tré trécorde trooked strings Très that's spell T-R accel conventional très vivid very lively troppo too much nant Mormont ol Bryan means not too fast una um uno one or Una corda, one string, un peu, a little. A working knowledge of these auxiliary terms will aid the student greatly in arriving at the meaning of hundreds of terms without stopping to look up at each individual one. Chapter 10 of Music Notation and Terminology. This is a LibriVox recording. All LibriVox recordings are in the public domain. For more information or to volunteer, please visit LibriVox.org. This recording by Karen Cummins. Music Notation and Terminology by Carl Wilson-Gurkins. Chapter 10, Measure 97. From the standpoint of the eye, a measure is that portion of the staff found between two bars. In certain cases, this space may be less than a measure, as, e.g., at the beginning and end of a movement. But from the standpoint of the ear, a single isolated measure is not possible, and the term must therefore be defined in the plural form. Measures are similarly accented groups of evenly spaced beats. Each group having at least one accented and one non-accented beat. The strongest accent falls normally on the first beat in the measure. Two essential characteristics are involved in the ordinary musical measure. One, a group of even beats, or pulses, always felt, though not always actually sounded. One or more of these beats being stronger than the rest. Two, certain rhythmic figures. Two eighth notes, a triplet, a dotted eighth and sixteenth note, four sixteenth notes, etc., which form the actual musical content of these groups. The student will note the essential difference between rhythm and measure. Rhythm is the regular recurrence of accent in a series of beats or pulses, while measure is the grouping of these beats according to some specified system. In listening to a piece of music, two hearers, A and B, may feel the rhythm equally strongly, but A may subjectively group the beats into one, two, one, two, etc., while B feels the group says one, two, three, four, one, two, three, four, etc. Rhythm is thus seen to be a fundamental thing inherent in the music itself, while measure is to a certain extent at least an arbitrary grouping which musicians have adopted for practical purposes. Ninety-eight. In syncopation, the normal system of accenting is temporarily suspended and the accented tone falls on the regularly unaccented part of the measure. Syncopation may therefore be defined as the temporary interruption of a normal series of accents, i.e. accenting a beat that is not usually accented. Thus, e.g. in figure fifty-six, measure one has the regular system of accents normally found in four-quarter measure, strong accent on one, secondary accent on three, but measure three has only one accent and it falls on the second beat. Ninety-nine. Measures are usually classified as simple and compound. A simple measure is one which has a single accent, i.e. the measure cannot be divided into smaller constituent groups. There are two main classes of simple measures, two-beat measure and three-beat measure. A compound measure is, as its name implies, one made up by combining two or more simple measures or by the elaboration of a single measure in slow tempo into several constituent groups. The principal compound measures are four-beat and six-beat, both being referred to as compound-duple measures. Five-beat, seven-beat, nine-beat and twelve-beat measures are also classified as compound measures. An English writer. Begin footnote twenty-three. Pierce, rudiments of musical knowledge, page thirty-seven. End footnote. Classifies measures as duple, triple or quadruple, specifying that a simple measure is one in which each beat is represented by a note whose value can be divided into halves. A quarter note equals two eighth notes. A half note equals two quarter notes, etc. And that a compound measure is one in which each beat is represented by a dotted note whose value can be divided into three parts. A dotted quarter note equals three eighth notes. A dotted half note equals three quarter notes. There is thus seen to be considerable difference of opinion as to the meaning of the words simple and compound when applied in this connection. The principal question at issue being whether four-beat measure is an individual variety or whether it is a variety compounded out of two-beat measures, either by placing two of these in a group or by the elaboration of a single measure into a larger number of beats as is often necessary in slow tempi. Perhaps the easiest way out of the difficulty is to admit that both may be true but in different compositions. That is, it is frequently impossible to tell whether a composition that is being listened to is in two-beat or in four-beat measure. And yet it is sometimes possible so to discriminate. Since however one cannot in the majority of cases distinguish between two-beat and four-beat measures, it will probably be best to leave the original classification intact and regard four-beat measure as a compound variety. 100. The commonest varieties of measure are one, duple, sometimes called even measure or even time, in which there are two beats, the first one being accented. Examples of duple measure are two over four, two over eight, two over two, two-quarter, begin footnote 24. For explanation of terminology, see page 48, section 106. In footnote 24. Two-eighth and two-half measure respectively. Two, triple, the old perfect measure in which there are three beats, the first one being accented, the second and third unaccented. Examples are three over eight, three over four, three over two, three-eighth, three-quarter and three-half measure respectively. Three, quadruple in which there are four beats, the first and third being accented, primary accented on one, secondary accented on three, the second and fourth unaccented. See note above under section 99. Four, sextuple in which there are six beats, the first and fourth being accented, the others not. In rapid tempi, this is always taken as compound duple measure, a dotted quarter note having a beat. It will be noted that the two measures, in six-eighth time measure A, six-eighth notes and measure B, two dotted quarter notes, are identical in effect with, in two-four time, two sets of triple eighth notes in measure A and in measure B, two quarter notes. 101. Other varieties of measure sometimes found are nine over eight and 12 over eight, but these are practically always taken as three-beat and four-beat measures respectively, being equivalent to these if each group of three tones is thought of as a triplet. In nine-eighth time, six-eighth notes followed by a dotted quarter is identical in effect with, in three-four time, two sets of eighth note triplets followed by a quarter note. 102. Quinn-tuple, five-beat and sep-tuple, seven-beat measures are occasionally met with, but these are rare and will always be sporadic. The five-beat measure is taken as a combination of three and two, or of two and three, sometimes a mixture of both in the same composition, while the seven-beat measure is taken in groups of four and three, or of three and four. 103. The sign that looks like C in an open measure is usually understood to mean four-quarter measure and the sign C with a vertical slash through it, two-half measure, but usage varies somewhat and the second sign is sometimes used to indicate four-half measure. It may be safely said, however, that the sign C with a vertical slash through it always indicates that a half note has a beat. Two C's with a vertical slash through it may occasionally be found indicating four-half measure, but this is rare. The student will note that the sign that looks like a C in an open measure is not a letter C, but an incomplete circle, differentiating two-beat and perfect measure from three-beat perfect measure. See appendix A, page 106. End of chapter 10. This recording was by Karen Cummins.


today we are going to cover the session on what is called probability plots I believe you all have experienced it or played with it and experimented with it during the R sessions which Professor Guru Rajan�보 technically introduce it to you as to what these plots are and what different kinds of plots are available. So first let us review what we have done in the past. We introduced random variable as a real value function with a probability space as its domain. Then we introduce expectations of this random variablemb해요. And re also introduce certain special random variables which have specific models of distribution. So, we introduce 2 kinds one is a discrete distribution functions in which we covered a Bernoulli trials binomial distribution geometric distribution negative binomial distribution and hyper geometric distribution. While in the continuous distribution function, we introduced uniform distribution function then normal distribution function, then some derivatives of normal distribution such as chi-square, p-distribution and f-distribution, we also introduced other distribution such as log normal distribution, viable distribution, exponential distribution. I must mention that there are many many many distributions available and many many new distributions are discovered in order to meet today's data requirement. But we have shown you a few of them which you come across more frequently and which will be useful to you in your immediate engineering requirement, immediate materials data requirement. Of course, as and when we move forward, the new distributions that we may require in the further analysis will be introduced in details there. Now in all these issue the question comes that we say that a random sample has been drawn from a distribution or specific distribution. How do we know that it really comes from that distribution? The reality picture is something like this. You have a very large population which you are trying to study. For example, if you are studying the yield strength of a particular alloy which is produced in a factory, in a industry then what how are you going to guarantee that it is going to have this particular yield strength? Well, the method is that you will take a few samples, random samples which you will choose them randomly not a systematically and then you will derive certain statistics and you will derive certain values and you would like to see if this distribution and you would have assumed that well, theoretically the yield strength should follow say log normal distribution or say normal distribution. Then the question remains is that does sample say that or not? This is the question we would like to answer in this session and this can be answered through what is known in statistics as goodness of fit tests. Goodness of fit tests are a very theoretical derivation of comparing the data values data CDF with the assumed CDF. But in the there is another method which is called a graphical method which does not give you a strong proof but it gives you a confirmatory guideline that yes it you are our assumption that this particular sample comes from this distribution may be correct in this scenario and this is what we would like to cover. We are not going to cover the theoretical goodness of fit tests in this course but we would like to cover some of the graphical methods for confirmatory guidelines. We are going to consider primarily two such graphical methods one is called probability plots or PP plots and the other is called a quantile plot which is known as queue queue plots. How do we go about doing this graphical comparison? We assume that data is coming is a sample from a particular distribution your data what you have got is a sample values coming from a particular assumed distribution. Hence naturally it means that whatever cumulative distribution function that you will obtain from data should match with the assumed distribution cumulative distribution function similarly if they are coming the sample data is coming truly coming from the one particular assumed distribution then the quantiles that we have calculated from the data should match with the theoretical quantiles that you would get from the assumed distribution. Such matching can be worked out in two ways if you are plotting the data CDF versus distribution CDF and if both are equal they should fall on a straight line so this is case one. The other one is if data quantiles if you plot against the assumed distribution theoretical quantiles then they should also match and they should fall on the straight line x is equal to y this is case two. So here I have detailed described PP plot CDF is calculated from the data and it is called an empirical CDF then another CDF is calculated from the assumed distribution and it is called a theoretical CDF. PP plot refers to plotting the empirical CDF on y axis and theoretical CDF on the x axis. If our assumption is true that the data is truly coming from the assumed distribution then the points on this plot should fall approximately on y is equal to x line otherwise we should be able to clearly see a mismatch. So let us see the two plots. Now in this plot what I have done is I have taken I have simulated standard normal variates using random number generator I have simulated about 100 of them and then I have calculated from that data the cumulative distribution function let us do some recalling here cumulative distribution function of data is nothing but number of data or let us call it a f of x less than or equal to t is nothing but number of data points less than or equal to t divided by n which is total data points. So this is called the empirical CDF ok.  So this is called theoretical CDF. So the values of this theoretical CDF on t is given here this is the next axis which gives the theoretical CDF. This empirical CDF is plotted on the y axis and that is plotted in that is shown in here. So if you take any typical value here this says that theoretical CDF which is in here this is your theoretical CDF value and this is your empirical CDF value. So this is how all these points are plotted and now what we say is that if your assumed distribution is the correct distribution for the data that is your data truly comes from the standard normal distribution which in this case we know because we have generated it randomly. You can see that it should fall on the line this is y is equal to x line. So it should fall approximately on y is equal to x line and you can see that these points are falling and therefore it says that ok it confirms graphically that the data point seem to be coming from the standard normal distribution. Let us take the case of mismatch because sometimes we understand only when we see the matching but more we understand if we see the mismatch. Now here we go here I have generated a log normal data by random number generator. So I have a log normal data generated log normal data generated from the normal from the random number generator and I am assuming that the data is actually coming from a viable distribution. I have generated the data so it means that I have a data from a population which actually has a distribution log normal while I have thought that I have actually drawn a sample from a viable distribution. I have very purposefully taken these two distributions together is because in the field of metallurgical parameters or properties such as strength property you take yield strength you can take UTS. We can consider even the fracture toughness there is always a question which distribution is closer and the two competitive distributions for all the strength of the strength property of the material is log normal and viable. So here I have taken the log normal and viable distribution as two competitive distributions. So I once again repeat what we have taken is we have taken a data actually from the log normal distribution but I have assumed or I have believed that the data is coming from the viable distribution then this becomes my theoretical distribution and this becomes my empirical distribution and I have plotted once again this shows the viable CDF and this shows the empirical log normal CDF that is it is only an empirical CDF it is not really log normal I have originally drawn the data from log normal. So please let us understand it clearly this is a data this is coming the empirical means that it is coming from data but for my understanding in this course I have generated this data from log normal CDF therefore I am writing log normal otherwise it is a data. So just as we did it in the previous case for data the empirical CDF is a ratio of number of data points less than or equal to t divided by total number of data. So this is your empirical CDF for value t and then this is a viable CDF which I call a this is calculated from the viable CDF distribution function and I call it a viable CDF and now you see that if I draw this line which is x is equal to y this is x is equal to y or y is equal to x line you see that the data is systematically falling above and falling below there is no random behavior I mean there is there is it is not an error difference as it happened in the previous case the data is systematically going above and then systematically going down and therefore we understand that there is a mismatch with your empirical CDF and your assumed CDF your assumed CDF is far away from what your data says and remember data is what we believe data is what we believe now let us consider understand the qq plot here again like CDF we take the quantiles of empirical distribution and we plot it against the quantiles of theoretical distributions okay you please recall what is quantile you have understood the quantile in terms of quartile okay we are talking about quantiles we have come across the definition of quartiles quartiles is such that first quartile q1 is such that probability of data x less than or equal to q1 is 0.25 quartile 2 is such that probability of x less than or equal to q2 is half and q3 is a third quartile where probability of x less than or equal to q3 is 0.75 so if you want to divide the data into four equal parts your data is here if you want to divide the data into four equal parts such that the probability from negative infinity to q1 q1 to q2 q2 to q3 and q3 onwards are all equal these are all equal probability and they are all 1 fourth this is what is called quartile and if you recall this is also known as median quantile is a general term so if you wish to have this probabilities your data be divided into say five equal parts then you will have if you want to divide it into five equal parts then you will have each of this there are six parts here right there is one two three four five and six so each one will have a probability one six so you will have a five values which I call p1 p2 p3 p4 and p5 then my this will be called pentile so if I take a first pentile p1 is such that probability that x is less than or equal to p1 is 1 over 6 and likewise p2 is such that probability of x less than or equal to p2 is one third or 2 over 6 likewise you can define so quantile is a general term if you want to consider the case of dividing the data into four equal probabilities you will have quartiles if you want to sorry these are not pentiles these are a hexiles if you want to divide it into six equal part it will have five points p1 p2 p3 p4 p5 which will divide each data into one sixth they are called hexiles you can have this isles you can have centeniles etc etc I mean you have 90% data here and there you mean there are various ways of doing it so in this way you can define a quantize in the example which I am going to show that there is a matching and there is a mismatch I am going to consider the size I am going to consider the size it means that the data will divided into 10 equal probability parts where each part will have a probability of 0.1 0.1 1 over 10 and when I define like this you remember it is a cumulative probability that I am defining so I am defining all the values here below this and therefore it becomes 2 times 1 over 6 okay so let us see the plots now so if you look at the plot again I have taken the same standard normal variates generate data generated by using random number generator and I have calculated their desiles so there are one sorry there are 1 2 3 4 5 6 7 8 and 9 points remember if it is a desile you are bringing it into 10 parts there will be 9 quantiles 9 desiles okay and these 9 desiles I have plotted if you take any typical 1 if you take any typical 1 this shows the data desile or as I have called it empirical quantiles and this is theoretical quantile calculated from normal 0 1 and I have plotted each value and you can see that there is a way deviation I have made the points very big but otherwise you can look at the center of these points and you know that they are little above on the line or little below etc because I am actually taking random number generated standard normal random generator using using random generator to generate the standard normal distribution now if you look at the mismatch again I have done the same thing I have taken the log normal distribution to generate random variables of log normal in other words I have used a random number generator and generated log normal random variables and I calculated quantiles and I am thinking that they have all come from Weibull distribution and I am comparing them so I am doing little bit of an artificial thing but this is to drive the point home I am following this random number generated values here so this is once again empirical desiles and these are Weibull desiles these are also desiles there are exactly 10 if you look at it there are 10 9 data points 3 and 3 is 6 and this 39 and you can see that very systematically it diverts away from the line which is x is equal to y and therefore it says that what you have assumed your data coming from is not the case your data is coming from some other distribution than the assumed distribution of Weibull once again I repeat that here we are comparing the empirical desiles with the Weibull desiles this is calculated from data so if I call d 1 as the first desile then d 1 is such that probability of data x is less than or equal to d 1 is 0.1 d 2 that is this is d 1 point this is d 2 then this d 2 is such that probability that x is less than or equal to d 2 is 0.2 and likewise so this is d 1 this is d 2 like this I have calculated the interesting part here is that in the previous case we were matching probability with probability here we are matching the data value with the data value so this is something strikingly different in this case there are other plots same plots are made in a different way for example instead of considering your x axis instead of considering your x axis as the actual quantiles or actual cdf and y axis also as cdf it says that you take y axis or x axis as the data values so x axis becomes the data values and y axis is taken as a theoretical probability scale there are when there were the computers were not so common when we studied statistics there used to be normal probability scale paper available in the market and y bull probability scale paper available in market now you don't need as you have done it in the r exercise you can very easily give a command as to what should be your y axis what theoretical probability scale you want and then it plots the data values against the theoretical probability value and again the matching has to be at x is equal to y so x is in the usual numeric scale showing the data probability values are plotted against the value of random variables that it takes and here also it falls on a y is equal to x line so the exercise that you have might have done in the descriptive statistics r sessions are largely using the probability scale as one of the as y axis and x as a data axis so let us summarize what we discussed today we talked about graphical methods to check if the distributional assumptions made on the data are matching or not matching if you plot an empirical cdf against the theoretical cdf it is called a pp plot if you plot a data quantiles against the theoretical quantiles then it is called a qq plot the same comparison can be made by plotting empirical cdf on the you can plot the empirical cdf using a probability plot papers and this probability papers i do not know if the market any more sells it but at least you can have it easily on any software package that does the statistical analysis in particular r has this facility in all the above cases it is a matching if it matches x is equal to y line if there is a mismatch then that is called a indicate a mismatch with your assumption and where the data comes from thank you