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Music Theory from Square One.

24K views 96 replies 30 participants last post by  aleazk 
#1 ·
In reply to a request for help with basic music theory, I have elected to start a thread which will act as a simple, unofficial tutorial on the subject. The idea is to have an open discussion based on the posts I'll be puting up here from time to time dealing with very basic music theory topics.

This first post should be up later today and I hope it will be helpful for a lot of the newcomers to this forum as well as entertaining for the more regular visitors.

See you later.
FC
 
#3 · (Edited)
For almost a thousand years western music has been written down. Despite being part of an aural tradition where songs and tunes were learned by ear or by someone showing someone else how to play a certain tune, the stuff of music (notes and chords etc.) at some point became too complex to be passed on in this manner. It became absolutely essential to be able to write down or 'notate' a piece of music.

Written down music is called 'music manuscript' and the system for writing it down in any way is called 'notation'.

Today's musicians in western culture use several 'notation systems' depending on which instrument and style they have in mind.

A guitarist might use any of three or four different types of notation:

1. A pictorial representation of the fretboard with dots showing where his fingers should be pressed down to form a certain chord (several notes sounding together).
2. A 'tabulation' where the strings of the instrument are each given instructions which the guitarist follow simutaneously.
3. A system of chord names abreviated into letters and numbers which he translates into the chords to be played. And finally
4. Actual 'standard musical notation' where the notes to be played are represented independantly of whether they are intended for guitar or not.

It is this fourth system that is the most widespread music notation system in use in western music today and it is the most useful for demonstrating all the features of western musical theory.

It was invented in the 10th century by an Italian monk called Giudo D'Arezzo and consists of several horizontal parallel lines which are read left to right and upon those lines are placed symbols (dots and lines) which represent notes (both in pitch and duration).

The set of parallel lines that has come down to us today is known as 'the stave' and looks like the first of the two diagrams below. 5 parallel lines.

In the second diagram there are 2 florid symbols which are called clefs (the French word for 'key') and helps the musician to work out which pitches are being refered to by the stave.
The first symbol is called the 'treble clef' and is centred on the second bottom line of the stave. Since the sign is based on the written letter 'G' as you can see below, the treble clef is sometimes called the 'G clef'. It indicates that the second bottom line of the stave represents the note 'g'. The dot on this line which follows is the note 'g'. We'll look at all the notes next time.

Also in the second diagram there is another symbol called the 'Bass clef' which is centred on the second top line of the stave. This symbol is based on the written letter 'F' and is sometimes called the 'F clef' and indicates that the second top line of the stave is the note F. The note following it in the diagram is the note f. Note that if the F clef had not been there the note would be considered as belonging to the treble clef which is at beginning of the line.

Next time we'll look at how different notes are written and how their lengths are notated.

Cheers
FC
 
#6 ·
The idea is to be really basic for absolute beginners without making anyone feel alienated by the depth of theoretical knowledge some here may have. So let's keep everything right down to a lowest common denominator as we go. Hopefully in a few weeks or months this will be a reference thread for newcomers.

I should thank sammyyooba for getting me started on this.

'Eighth notes' and 'quarter notes' are names given to certain note lengths. That is to say a word that describes the duration of the note but only relative to the speed of the music and not an absolute measurement in seconds. It is easy to guess that in the same piece an 'eighth note' will last half as long as a 'quarter note' which is only half as long as a 'half note' and so on. In England the old French words for relative note lengths are still in use.

A half note = a 'minim'
a quarter note = 'crotchet'
an eighth note = 'quaver'

so you can now see the full story behind the references to 'two crotchets = a minim' etc.

I will use the american system of calling the note lengths after their 'fraction' names. That is eighth, quarter, sixteenth etc. because it is easier to imagine and it is more universally accepted.

FC
 
#8 ·
I'll be very interested to see at what point I drop out of this (brilliant idea Fergus, by the way). In my time I've acquired a passable understanding of general relativity and quantum mechanics, but music theory, despite many attempts - never. I know what will happen - I shall follow you perfectly well through these elementary stages, and then at some point in the future I shall meet a brick wall of incomprehension, and there'll be no crossing it. Reading a score (unless it be Three Blind Mice in C major for treble recorder) still seems as utterly impossible as flying.

I think it's one of those dodgy brain-wiring things that some people experience with regard to mathematics. But lead on, Fergus, lead on. I will follow till I drop.
 
#9 ·
I too attempted to teach myself music theory and tho I struggle to read notation(and can't get away with tab at all) i find the theory fascinating. I got quite into it,learning about T,T,T,st,T,T,st etc but then kids came along and that was that! Game over.
 
#13 ·
2. Notes.

Now that we have seen the 'stave', the place where most western music is written down, it's time to look at exactly what is written there and how that relates to what musicians play as they read it.

Music notation is like a written language in as much as it is a set of symbols which represent sound which can be translated into sound. In the case of language these sounds are spoken, in the case of music they are sung or played. Whereas a language has letters, words and sentences, music has its constituent parts such as notes, chords, melodies, phrases etc. We will see exactly what they are in due course, first let's see some notes.

When you sing, you sing notes, no matter how badly or untrained you might be. Almost anyone can do this, but a trained musician will be able to make controlled changes to his or her voice to produce a melody and not just any melody but a melody which as been written down by another musician (possibly from another country and even a different time), rather like reading a book by Dostoyevsky. There is no need to have Dostoyevsky in front of us to tell his stories. He 'wrote them down' and now we can 'read' them anytime we like. In the same way Beethoven, Mozart and all the other great composers of western music have written down their music in order that they don't have to stick around to play it to us when we want to hear it. Imagine having to ask Beethoven round so you could hear his ninth symphony!

So what do these musical symbols look like and what do they mean? Like letters and words on the page, notes on the stave have different shapes and placements. Let's have a look at what a note you might sing could look like:



That's it there, the first dot! Of course this may not be very accurate because not everyone will sing exactly the same thing, but I imagine that you all might sing a note and hold it for a second or two and then stop. That's what you are seeing here. It looks like a black dot sitting somewhere on the stave with a tail going off vertically. The dot, or 'note head' has to be written in such a way that you can tell exactly where it sits, vertically on the stave. If it were a huge dot (like the second dot) then you could not say if it was on the second bottom line or in the first space or whatever. If it was tiny (like the third dot) then it might not show up if it was on a line! So the dot has to be a bit bigger than the thickness of the stave lines but smaller or equal to than the distance between the stave line.

This makes it easy to see where the note sits vertically on the stave. This is very important because it is the key to telling which note is being symbolised!
Remember in the first post we looked at the G clef where the florid G symbol was centred on the second bottom line of the stave? Well that is the key to working out which note is being symbolised. First let me tell you how the notes themselves are named.

In western music different countries use different systems to name notes and some times even professional musicians form different coutries get confused when discussing music that they are playing. What a French man calls 'Si' in what an Englishman calls 'B' and what an Englishman calls 'C' is what a Frenchman calls 'Do', and what an Englishamn calls 'Dough' the Frenchman calls l'argent! (Humour aside.)

I will use the accepted English language system for naming the notes so let's see how that works.

Here are all the notes that fall within the stave in order from lowest to highest. Below the notes are their names as used in the English system.



As you can see the lowest note is E and the next F followed by G. The next note, however, is called A! Why is that?

Well in this system we use seven letters A,B,C,D,E,F and G to name the notes as they appear on the stave without any exrta infromation (we'll see what kind of information this can bee when we look at 'accidentals' a bit latter). If you remember that the florid 'G cleff' or "treble clef' (which is what we will call it from now on) is written on the second line of the stave so, naturally a note on that line would be a 'G'. Everything is relative to this point - so the note written in the space just below the 'G' line is an 'F', and the note written on the line below the 'F' space is an 'E'. Notes written above the 'G' line start over using the series A,B,C,D,E,F and G again. So the note written in the second space (the one just above the 'G' line) is an 'A'. If you look at the diagram again you can see all the names of the notes that fall within the stave.

You might think that the diagram looks like a fight of stairs. Well you're right! The musical word for what you're seeing here is a 'scale'. A lot of western music is built using certain series of notes called 'scales'. The word means 'steps' and comes from the Italian 'scalla', like the famous opera house, the 'Teatro la Scalla' in Milan, which is called literally 'the Theatre of the Steps'.

Here's a bit of ancient history:

We'll take a quick trip back in time about 2500 years to the Island of Samos in the Aegean Sea. There we find the great mathematician and philosopher Pythagoras. He was the one who told us how to measure triangles if you remember, but besides that he was also an avid observer of nature. One of the things that Pythagoras noticed was that when he hung his boots up by the laces they swung in accordance to the length of the lace. The longer the lace the slower the swing. Now he was also a lute player (the lute is a bit like a small harp) and he knew that the longer his lute string was, the 'lower' in pitch the note would be. After looking at all this together he decided to see what the mathematical relationship was between the notes and the speed of the swing and the length of the string etc.

To do this he built a thing called a 'monochord' which just means, 'one string' which is in fact all it was: a box with one string stretched over it.



Here you can see that there is a 'moveable bridge' supporting the string. (A 'bridge' is the part of a stringed instrument that supports the string.) Pythagoras would measure the length of the string at various points and try to find out which notes came out of his monochord. He was delighted to find that there was a mathematical relationship between the length of the string and the pitch of the note. He discovered that when a string is pucked it produces a note of a certain pitch which is the result of the string swinging back and forth quickly (called 'oscilation' or 'vibration') and that when it was only half of the original length it would produce a sound that was in many ways very similar to the original but somehow higher in pitch. He worked out that to produce this effect the number of 'oscilations' was exactly double!

With this in mind he decided to shorten the string length to a third of the original and found that the note changed all together but when both the original string and the third of the length string were struck at the same time the sound was very rich and pleasing.

Pythagoras believed that the universe was ruled by numbers and decided to experiment further by dividing the string into quarters and fifths and sixths etc of it's original length. Doing so he discovered that each division sounded slightly different and some would not sound good together and others sounded lovely.

Ultimately he found that he could make divisions in string length up to about a twelfth and still find someway of combining the resulting sounds together. He then built a monochord which could artificially divide the string into proprtions of it's original lengths by use of 'frets'. Frets are the lines you see on the neck of a guitar and they are almost exactly in the places that Pythagoras would have put them if he made guitars today!

The strange strange simlalrity between a one string and another half it's length in called an 'Octave' You can hear this phenomena on a guitar by playing the string without any fingers pressing down and then pressing down your finger on the half way mark and playing the free part of the string again. This was so much an itegral part of the pythagorean way of thinking that even today at meetings of Pythagoreans the 'sounding of the octave' is used to signify the beginning of their council.

Now, going back to the diagram of the scale, the notes E on the bottom line and E in the top space have the same name but they are written in different places. They are related to each other by the 'interval' of an octave (the thing Pythagoras was nuts about!). An 'interval' is the distance between two notes and that is one of the many things we'll look at next time.

FC
 
#17 ·
Is there anyone else with sufficient knowledge to continue?
I wouldnt mind continuing on to basic harmony/circle of fifths.
 
#18 ·
I'm not nearly eloquent enough, myself. I just know how it works, how to write it down, different harmonic structures, etc.

We could go over format for pieces starting as simple as ABA format, though.
 
#20 · (Edited)
Here's some info on composition formats:

Levels of organization

The most basic levels of musical form concern (a) the arrangement of the pulse into accented and unaccented beats, the cells of a measure that, when harmonized, may give rise to the "briefest intelligible and self-existent musical unit" (Scholes, 1977), called a motif or figure, and (b) the further organization of such a measure, by repetition and variation, into a true musical phrase having a definite rhythm and duration that may be implied in melody and harmony, defined, for example, by a long final note and a breathing space. This "phrase" may be regarded as the fundamental formal unit of music: it may be broken down into measures of two or three beats but its distinctive nature will then be lost. Even at this level we can see the importance of the principles of repetition and contrast, weak and strong, climax and repose. (Macpherson 1930). (See also: Metre (music)) Given all this, we may understand the term "form" on three further main levels of organization that we can roughly designate "passage", "piece", and "cycle" for purposes of exposition:

Passage

The smallest level of construction concerns the way musical phrases are organised into musical "sentences" and "paragraphs" such as the verse of a song. This may be compared to, and is often decided by, the verse-form or metre of the words or the steps of a dance.

For example, the twelve bar blues is a specific verse form, while common metre is found in many hymns and ballads and, again, the Elizabethan galliard, like many dances, requires a certain rhythm, pace and length of melody to fit its repeating pattern of steps. Simpler styles of music may be more or less wholly defined at this level of form, which therefore does not differ greatly from the loose sense first mentioned and which may carry with it rhythmic, harmonic, timbral, occasional and melodic conventions.

In the analysis of musical form, sections, units etc. that can be defined on the time axis are conventionally designated by letters, as is the case in discussing poetic form. Capitals are used for the most fundamental, lower-case for sub-divisions. If one such section returns in a varied or modified form, a small digit or an appropriate number of prime symbols appears after the letter. Even at this most basic level we find patterns that may be re-used on larger time-scales. For example, the following verse:

Twinkle twinkle little star
How I wonder what you are
Up above the world so high
Like a diamond in the sky.


has a verse composed of two differently-rhymed couplets (AABB): its organisation is twofold or binary. But in this one:

There once was a fellow from Leeds
Who swallowed a packet of seeds.
In less than an hour he burst into flower
And he died trying to pull up the weeds.


there is a rhyme repeated in the second line, but in the third we find a variant, two half-lines sharing a new rhyme, followed by a final return to the first arrangement in the last line, giving the four lines the form AABA. This "same-different-same" form in music is called ternary or threefold. However, as Macpherson points out (1930) there is a preference at all levels of musical organization for groupings of two, four, eight over other divisions, so that even a "threefold" form is often extended by repetition of the first subject into a fourfold structure. Composers, in fact, must be on guard against excessive "squareness".
 
#21 · (Edited)
And we soldier on:

Piece

The next level concerns the entire structure of any single more or less self-contained musical piece. If the hymn, ballad, blues or dance alluded to above simply repeats the same musical material indefinitely then the piece is said to be in strophic form overall. If it repeats with distinct, sustained changes each time, for instance in setting, ornamentation or instrumentation, then the piece is a Theme and variations. If two distinctly different themes are alternated indefinitely, as in a song alternating verse and chorus or in the alternating slow and fast sections of the Hungarian czardas, then this gives rise to a simple two-fold or binary form. If the theme is played (perhaps twice), then a new theme is introduced, the piece then closing with a return to the first theme, we have a simple ternary form. - (see Single forms below)

Great confusion, argument and misunderstanding can be generated by such terms as "ternary" and "binary", however, since a complex piece may have elements of both at different organizational levels. For example, a simple minuet, like any Baroque dance, generally had a simple AABB binary structure - but this was frequently extended by the introduction of another minuet arranged for solo instruments (called the trio), after which the first was repeated again and the piece ended. This, of course, is a ternary form - ABA: the piece is binary on the lower compositional level but ternary on the higher. Organizational levels are not clearly and universally defined in western musicology, while words like "section" and "passage" are used at different levels by different scholars whose definitions, anyway, as Scholes (1977) and others point out, cannot keep pace with the myriad innovations and variations devised by musicians.

Single forms

Scholes (1977) suggested that European classical music had only six main stand-alone forms; simple binary, simple ternary, compound binary, rondo, air with variations, and fugue, although he allowed for several sub-categories and hybrids. Mann (1958), however, while confirming that the fugue has taken on certain structural conventions at times, emphasized that it is primarily a method of composition.

Where a piece cannot readily be broken down into sectional units (though it might borrow some form from a poem, story or programme) It is said to be through-composed. Such is often the case with pieces named Fantasia, Prelude, Rhapsody, Etude or study, Symphonic poem, Bagatelle (music), Impromptu etc.

Keil (1966) classified forms and formal detail as sectional, developmental or variational.

Sectional form is built from a sequence of clear-cut units (DeLone, 1975) that may be referred to by letters as outlined above but also often have generic names such as Introduction and Coda, Exposition, Development and Recapitulation, Verse, Chorus or Refrain and Bridge. Introductions and codas, when they are no more than that, are frequently excluded from formal analysis. All such units may typically be eight measures long. Sectional forms include:

* Strophic form (AAAA...) indefinitely - the "unrelieved repetition" that is one extreme of the spectrum of musical form.

* Medley, potpourri or Chain form: this is the opposite extreme of "unrelieved variation": it is simply an indefinite sequence of self-contained sections (ABCD...), sometimes with repeats (AABBCCDD...). Orchestral overtures, for example, are sometimes no more than a string of the best tunes of the show to come, possibly, like Johann Strauss' Blue Danube waltz, ending with a reprise of the main theme; ((intro)ABCD...A1(coda)).

* Binary form using two sections (AB...); each section is often repeated (AABB...). In 18th-century western classical music simple binary form was often used for dances and carried with it the convention that the two sections should be in different musical keys but maintain the same rhythm, duration and tone. The alternation of two tunes gives enough variety to permit a dance to be extended for as long as may be required.

* Ternary form, having three parts. In Western classical music a simple ternary form has a third section that is a recapitulation of the first (ABA). Often the first section is repeated (AABA) This approach was popular in the 18th-century operatic aria and was called da capo (i.e. "repeat from the top") form: later it gave rise to the 32-bar song, the B section then often being called the "middle eight". A song has more need than a dance of a self-contained form with a beginning and an end.

* Rondo form has a recurring theme alternating with different (usually contrasting) sections called episodes. It may be asymmetrical (ABACADAEA) or symmetrical (ABACABA). A recurring section, especially the main theme, is sometimes more thoroughly varied, or else one episode may be a development of it. A similar arrangement is the Ritornello form of the baroque concerto Grosso. Arch form (ABCBA) resembles a symmetrical rondo without intermediate repetitions of the main theme.
 
#22 ·
We continue here once again:

Cyclical forms

Opera was originally modeled upon classical drama and takes much of its form from its libretto and narrative. Ballet was for many years a component of opera, not in itself narrative but having the form of a suite of set dances included at some appropriate moment in the story such as a festival or wedding. It emerged as a separate form, supplying its own narrative or representation, during the nineteenth century CE. At the same time the Song cycle emerged, a set of related songs as the suite is a set of related dances. The Oratorio took shape as a narrative, often religious, recounted but not acted by the singers.

The Sonata, Symphony and Concerto were all developed by the great composers of the Viennese school, Haydn, Mozart and Beethoven along the same formal lines into distinctively musical forms limited little by the forms of song, dance or ceremony. Other forms of music, such as the Catholic Mass and Requiem, are largely shaped by and subordinated to their texts and ceremonial functions.
 
#23 ·
Some more info:

More recent developments

A common idea is the "depth" of layers of form necessary for complexity, in which foregrounded "detail" events occur against a more structural background, as in Schenkerian analysis. Lerdahl (1992), among others, argues that popular music lacks the structural complexity of multiple structural layers and thus lacks depth. However, Lerdahl's theories explicitly exclude "associational" details which are used to help articulate form in popular music, which Allen Forte's book theories were designed to analyze. (Middleton 1999, p. 144).

Western classical music is the apodigm of the extensional form of musical construction. Theme and variations, counterpoint, tonality (as used in classical composition) are all devices that build diachronically and synchronically outwards from basic musical atoms. The complex is created by combination of the simple, which remains discrete and unchanged in the complex unity...If those critics who maintain the greater complexity of classical music specified that they had in mind this extensional development, they would be quite correct...Rock however follows, like many non-European musics, the path of intensional development. In this mode of construction the basic musical units (played/sung notes) are not combined through space and time as simple elements into complex structures. The simple entity is that constituted by the parameters of melody, harmony, and beat, while the complex is built up by modulation of the basic notes, and by inflexion of the basic beat. All existing genres and sub-types of the Afro-American tradition show various forms of combined intensional and extensional development.
-Chester 1970, p.78-9

Similarly, (Middleton 1990, p. 115) maintains that "syntactic music" is "centered" on notation and "the hierarchic organization of quasilinguistic elements and their putting together (com-position) in line with systems of norms, expectations, surprises, tensions and resolutions. The resulting aesthetic is one of 'embodied meaning.'" on the other hand, non-notated music and performance "foreground process and are concerned with gesture, physical feel, the immediate moment, improvisation; the resulting aesthetic is one of 'engendered feeling' and is unsuited to the application of 'syntactic' criteria".

Connection and contrast may be achieved in new ways. Procedures of connection include gradation, amalgamation, and dissolution. Procedures of contrast include stratification, juxtaposition, and interpolation.

Especially recently, more segmented approaches have been taken through the use of stratification, superimposition, juxtaposition, interpolation, and other interruptions and simultaneities. Examples include the postmodern "block" technique used by composers such as John Zorn, where rather than organic development one follows separate units in various combinations. These techniques may be used to create contrast to the point of disjointed chaotic textures, or, through repetition and return and transitional procedures such as dissolution, amalgamation, and gradation, may create connectedness and unity. Composers have also made more use of open forms such as produced by aleatoric devices and other chance procedures, improvisation, and some processes.
 
#24 ·
And now we tackle each form individually to end it for today:

Gregorian Chant-Melodic types

Gregorian chant is of course vocal music. The text, the phrases, words and eventually the syllables, can be sung in various ways. The most straightforward is recitation on the same tone, which is called "syllabic" as each syllable is sung to a single tone. Likewise, simple chants are often syllabic throughout with only a few instances where two or more notes are sung on one syllable. "Neumatic" chants are more embellished and ligatures, a connected group of notes, written as a single compound neume, abound in the text. Melismatic chants are the most ornate chants in which elaborate melodies are sung on long sustained vowels as in the Alleluia, ranging from five or six notes per syllable to over sixty in the more prolix melismas.[22]

Gregorian chants fall into two broad categories of melody: recitatives and free melodies.[23] The simplest kind of melody is the liturgical recitative. Recitative melodies are dominated by a single pitch, called the reciting tone. Other pitches appear in melodic formulae for incipits, partial cadences, and full cadences. These chants are primarily syllabic. For example, the Collect for Easter consists of 127 syllables sung to 131 pitches, with 108 of these pitches being the reciting note A and the other 23 pitches flexing down to G.[24] Liturgical recitatives are commonly found in the accentus chants of the liturgy, such as the intonations of the Collect, Epistle, and Gospel during the Mass, and in the direct psalmody of the Office.

Psalmodic chants, which intone psalms, include both recitatives and free melodies. Psalmodic chants include direct psalmody, antiphonal chants, and responsorial chants.[25] In direct psalmody, psalm verses are sung without refrains to simple, formulaic tones. Most psalmodic chants are antiphonal and responsorial, sung to free melodies of varying complexity.

Antiphonal chants such as the Introit, and Communion originally referred to chants in which two choirs sang in alternation, one choir singing verses of a psalm, the other singing a refrain called an antiphon. Over time, the verses were reduced in number, usually to just one psalm verse and the Doxology, or even omitted entirely. Antiphonal chants reflect their ancient origins as elaborate recitatives through the reciting tones in their melodies. Ordinary chants, such as the Kyrie and Gloria, are not considered antiphonal chants, although they are often performed in antiphonal style.

Responsorial chants such as the Gradual, Alleluia, Offertory, and the Office Responsories originally consisted of a refrain called a respond sung by a choir, alternating with psalm verses sung by a soloist. Responsorial chants are often composed of an amalgamation of various stock musical phrases, pieced together in a practice called centonization. Tracts are melismatic settings of psalm verses and use frequent recurring cadences and they are strongly centonized.

Gregorian chant evolved to fulfill various functions in the Roman Catholic liturgy. Broadly speaking, liturgical recitatives are used for texts intoned by deacons or priests. Antiphonal chants accompany liturgical actions: the entrance of the officiant, the collection of offerings, and the distribution of sanctified bread and wine. Responsorial chants expand on readings and lessons.[26]

The non-psalmodic chants, including the Ordinary of the Mass, sequences, and hymns, were originally intended for congregational singing.[27] The structure of their texts largely defines their musical style. In sequences, the same melodic phrase is repeated in each couplet. The strophic texts of hymns use the same syllabic melody for each stanza.
 
#25 ·
Gregorian Chants continued:

Modality

Early plainchant, like much of Western music, is believed to have been distinguished by the use of the diatonic scale. Modal theory, which postdates the composition of the core chant repertory, arises from a synthesis of two very different traditions: the speculative tradition of numerical ratios and species inherited from ancient Greece and a second tradition rooted in the practical art of cantus. The earliest writings that deal with both theory and practice include the Enchiriadis group of treatises, which circulated in the late ninth century and possibly have their roots in an earlier, oral tradition. In contrast to the ancient Greek system of tetrachords (a collection of four continuous notes) that descend by two tones and a semitone, the Enchiriadis writings base their tone-system on a tetrachord that corresponds to the four finals of chant, D, E, F, and G. The disjunct tetrachords in the Enchiriadis system have been the subject of much speculation, because they do not correspond to the diatonic framework that became the standard Medieval scale (for example, there is a high F#, a note not recognized by later Medieval writers). A diatonic scale with a chromatically alterable b/b-flat was first described by Hucbald, who adopted the tetrachord of the finals (D, E, F, G) and constructed the rest of the system following the model of the Greek Greater and Lesser Perfect Systems. These were the first steps in forging a theoretical tradition that corresponded to chant.

Around 1025, Guido d'Arezzo revolutionized Western music with the development of the gamut, in which pitches in the singing range were organized into overlapping hexachords. Hexachords could be built on C (the natural hexachord, C-D-E^F-G-A), F (the soft hexachord, using a B-flat, F-G-A^Bb-C-D), or G (the hard hexachord, using a B-natural, G-A-B^C-D-E). The B-flat was an integral part of the system of hexachords rather than an accidental. The use of notes outside of this collection was described as musica ficta.

Gregorian chant was categorized into eight modes, influenced by the eightfold division of Byzantine chants called the oktoechos.[28] Each mode is distinguished by its final, dominant, and ambitus. The final is the ending note, which is usually an important note in the overall structure of the melody. The dominant is a secondary pitch that usually serves as a reciting tone in the melody. Ambitus refers to the range of pitches used in the melody. Melodies whose final is in the middle of the ambitus, or which have only a limited ambitus, are categorized as plagal, while melodies whose final is in the lower end of the ambitus and have a range of over five or six notes are categorized as authentic. Although corresponding plagal and authentic modes have the same final, they have different dominants.[29] The existent pseudo-Greek names of the modes, rarely used in medieval times, derive from a misunderstanding of the Ancient Greek modes; the prefix "Hypo-" (under, Gr.) indicates a plagal mode, where the melody moves below the final. In contemporary Latin manuscripts the modes are simply called Protus authentus /plagalis, Deuterus, Tritus and Tetrardus: the 1st mode, authentic or plagal, the 2nd mode etc. In the Roman Chantbooks the modes are indicated by Roman numerals.

Modes 1 and 2 are the authentic and plagal modes ending on D, sometimes called Dorian and Hypodorian.
Modes 3 and 4 are the authentic and plagal modes ending on E, sometimes called Phrygian and Hypophrygian.
Modes 5 and 6 are the authentic and plagal modes ending on F, sometimes called Lydian and Hypolydian.
Modes 7 and 8 are the authentic and plagal modes ending on G, sometimes called Mixolydian and Hypomixolydian.

Although the modes with melodies ending on A, B, and C are sometimes referred to as Aeolian, Locrian, and Ionian, these are not considered distinct modes and are treated as transpositions of whichever mode uses the same set of hexachords. The actual pitch of the Gregorian chant is not fixed, so the piece can be sung in whichever range is most comfortable.

Certain classes of Gregorian chant have a separate musical formula for each mode, allowing one section of the chant to transition smoothly into the next section, such as the psalm tones between antiphons and psalm verses.[30]

Not every Gregorian chant fits neatly into Guido's hexachords or into the system of eight modes. For example, there are chants-especially from German sources-whose neumes suggest a warbling of pitches between the notes E and F, outside the hexachord system.[31] Early Gregorian chant, like Ambrosian and Old Roman chant, whose melodies are most closely related to Gregorian, did not use the modal system.[32] The great need for a system of organizing chants lies in the need to link antiphons with standard tones, as in for example, the psalmody at the Office. Using Psalm Tone i with an antiphon in Mode 1 makes for a smooth transition between the end of the antiphon and the intonation of the tone, and the ending of the tone can then be chosen to provide a smooth transition back to the antiphon. As the modal system gained acceptance, Gregorian chants were edited to conform to the modes, especially during 12th-century Cistercian reforms. Finals were altered, melodic ranges reduced, melismas trimmed, B-flats eliminated, and repeated words removed.[33] Despite these attempts to impose modal consistency, some chants-notably Communions-defy simple modal assignment. For example, in four medieval manuscripts, the Communion Circuibo was transcribed using a different mode in each.[34]
 
#26 ·
And the 3rd part on Gregorian Chants (soldier on some more, we're almost through!):

Musical idiom

Several features besides modality contribute to the musical idiom of Gregorian chant, giving it a distinctive musical flavor. Melodic motion is primarily stepwise. Skips of a third are common, and larger skips far more common than in other plainchant repertories such as Ambrosian chant or Beneventan chant. Gregorian melodies are more likely to traverse a seventh than a full octave, so that melodies rarely travel from D up to the D an octave higher, but often travel from D to the C a seventh higher, using such patterns as D-F-G-A-C.[35] Gregorian melodies often explore chains of pitches, such as F-A-C, around which the other notes of the chant gravitate.[36] Within each mode, certain incipits and cadences are preferred, which the modal theory alone does not explain. Chants often display complex internal structures that combine and repeat musical subphrases. This occurs notably in the Offertories; in chants with shorter, repeating texts such as the Kyrie and Agnus Dei; and in longer chants with clear textual divisions such as the Great Responsories, the Gloria, and the Credo.[37]

Chants sometimes fall into melodically related groups. The musical phrases centonized to create Graduals and Tracts follow a musical "grammar" of sorts. Certain phrases are used only at the beginnings of chants, or only at the end, or only in certain combinations, creating musical families of chants such as the Iustus ut palma family of Graduals.[38] Several Introits in mode 3, including Loquetur Dominus above, exhibit melodic similarities. Mode III (E authentic) chants have C as a dominant, so C is the expected reciting tone. These mode III Introits, however, use both G and C as reciting tones, and often begin with a decorated leap from G to C to establish this tonality.[39] Similar examples exist throughout the repertory.
 
#27 ·
To stave off any accusations of plagiarism (I hate plagiarism as much as any other bloke), these quotes are from Wikipedia (which itself also quoted from a book on composition). So we have a double quote, here:) And now, our final segment on the Gregorian Chant (if anyone has enjoyed these brackets of information as much as me, just let me know and I'll continue with the rest of the musical forms):

Notation

The earliest notated sources of Gregorian chant (written ca. 950) used symbols called neumes (Gr. sign (of the hand) to indicate tone-movements and relative duration within each syllable. A sort of musical stenography that seems to focus on gestures and tone-movements but not the specific pitches of individual notes, nor the relative starting pitches of each neume. Given the fact that Chant was learned in an oral tradition in which the texts and melodies were sung from memory, this was obviously not necessary. The neumatic manuscripts display great sophistication and precision in notation and a wealth of graphic signs to indicate the musical gesture and proper pronunciation of the text. Scholars postulate that this practice may have been derived from cheironomic hand-gestures, the ekphonetic notation of Byzantine chant, punctuation marks, or diacritical accents.[40] Later adaptations and innovations included the use of a dry-scratched line or an inked line or two lines, marked C or F showing the relative pitches between neumes. Consistent relative heightening first developed in the Aquitaine region, particularly at St. Martial de Limoges, in the first half of the eleventh century. Many German-speaking areas, however, continued to use unpitched neumes into the twelfth century. Additional symbols developed, such as the custos, placed at the end of a system to show the next pitch. Other symbols indicated changes in articulation, duration, or tempo, such as a letter "t" to indicate a tenuto. Another form of early notation used a system of letters corresponding to different pitches, much as Shaker music is notated.

By the 13th century, the neumes of Gregorian chant were usually written in square notation on a four-line staff with a clef, as in the Graduale Aboense pictured above. In square notation, small groups of ascending notes on a syllable are shown as stacked squares, read from bottom to top, while descending notes are written with diamonds read from left to right. When a syllable has a large number of notes, a series of smaller such groups of neumes are written in succession, read from left to right. The oriscus, quilisma, and liquescent neumes indicate special vocal treatments, that have been largely neglected due to uncertainty as to how to sing them. Since the 1970s, with the influential insights of Dom. E. Cardine (see below under 'rhythm'), ornamental neumes have received more attention from both researchers and performers.

B-flat is indicated by a "b-mollum" (Lat. soft), a rounded undercaste 'b' placed to the left of the entire neume in which the note occurs. When necessary, a "b-durum" (Lat. hard), written squarely, indicates B-natural and serves to cancel the b-mollum . This system of square notation is standard in modern chantbooks.
 
#30 ·
can anyone help me?

I'm having problems understanding the relation of the intervals of a major scale:

The interval of the major scale:

notes half steps to next note

Tonic 2
second 2
third 1
fourth 2
fifth 2
sixth 2
seventh 1

in other words it goes.. whole, whole, half, whole,whole, whole, half. right?

now, when i look at the major scales i cannot point out the "half-steps to next note"
ex: C-sharp Major

it starts in C#, the next note is D#.. after is E#

to me, it's seems more like the interval is just a half-step
i can't figure this out.. =/

anyways, thanks in advance!
 
#36 ·
can anyone help me?

I'm having problems understanding the relation of the intervals of a major scale:

The interval of the major scale:

notes half steps to next note

Tonic 2
second 2
third 1
fourth 2
fifth 2
sixth 2
seventh 1

in other words it goes.. whole, whole, half, whole,whole, whole, half. right?

now, when i look at the major scales i cannot point out the "half-steps to next note"
ex: C-sharp Major

it starts in C#, the next note is D#.. after is E#

to me, it's seems more like the interval is just a half-step
i can't figure this out.. =/

anyways, thanks in advance!
I'm sorry I didn't see that post. Any other questions will be answered promptly. And mondo thanks to PostMinimalist for answering your questions correctly.
 
#31 ·
Well, it's probably a little easier to think in Db instead of C# at that point (though it's possible)

Db - Eb - F makes a lot more sense to me than C# - D# - E#

Remember...E# is F.

But a C# major scale is: C# - D# - E# - F# - G# - A# - B# - C# (all sharps!)
 
#33 ·
Yes, the order you had was correct. W-W-H-W-W-W-H

So C# to D# is a whole step (2 half steps). D# to E# (F enharmonically) is a whole step. E# to F# is a half step. F# to G# is a whole step. G# to A# is a whole step. A# to B# (C enharmonically) is a whole step. B# to C# is a half step.
 
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