Saturday, July 25, 2020

Musical sounds - 2 - Tonality and relations

Various tonal aspects of musical sounds, tonality and how it relates sounds in different musical styles of the world. 

This is the second of a 3 part post on musical sounds in music, for the first part please see here, and for the third part please see here.

I am interested in music and dance in general, and while enjoying various styles of these, I also find basic similarities between them to be very beautiful. I will also share some things that I personally like and find interesting in certain styles of music, and discuss my aesthetic preferences in general.

Harmonic tonality and chords 

Music may use sounds of more than one pitch (in sharply pitched instruments) playing simultaneously. A group of pitches within an octave (so not a unison) is called a chord. Music that uses chords, depends on the relations between the pitches playing together. These relations of consonance and dissonance are given by harmony and since they are based on pitches simultaneously playing, or combined, they are a more vertical organisation. This vertical heirarchy determines the horizontal forward movement of pitches. Harmony is used in many regions of the world including Europe, Caucasus, North, Central and South America, Australia (through European influence), Oceania and many regions of Sub Saharan Africa (independently). Generally the chromatic scale is a good pitch space for harmony since smaller intervals than semitones become too small to give harmonic movement. But even the chromatic scale is almost never completely used in harmonic tonal music. More separation between notes is generally needed for clearer movement and harmonic relations. So generally only subsets of 5, 6, 7 notes (pentatonic, hexatonic, heptatonic scales) are used, but with sometimes added pitches for variety. For this, as mentioned before, many semitones (and even microtones when used) are grouped under a single scale degree, and generally only one pitch/inflection of a scale degree appears contiguously. Since the European or Western system of harmony is most influential, it could be used as a reference. Fixing a tonic pitch and using harmonic relations (leaving extreme dissonance of semitone with the tonic), we can get two heptatonic (7 note) scales from the chromatic scale - major and minor. The major scale is tonic - major second - major third - fourth - fifth/dominant - major sixth - major seventh and the minor scale is tonic - major second - minor third - fourth - fifth/dominant - minor sixth - minor seventh. Although, these may be changed to highlight different harmonic relations while rising or descending in a scale, and the rising and descending scales need not be the same. Observing the main or first few overtones (which means that they are effective consonances with the fundamental frequency), we can see that having consonance in thirds (third scale degrees), from a pitch (first degree) to its third, can give a basis for harmonic relations. This third can be either major or minor in inflection, corresponding to pitches from the major and minor scales. Each of these gives a different relation. So chords can be formed by using a group of pitches with pairs having a consonant relation of a third, major or minor, between them. Other harmonic consonance relations may also be used in various styles of harmonic music. Generally, chords are considered only with three pitches playing together. Less than this, 2 simultaneous pitches, give a dyad, in which two consonant pitches may be combined. However, when a tonic is known, a dyad may imply some harmonic relations of a chord. 

A chord with 3 notes is called a triad, and using the relation of thirds, we get major and minor triads, which have tonic - major third - dominant (major triad) and tonic - minor third - dominant (minor triad) respectively, since the interval between a major (respectively minor) third and dominant is equal to the interval between a tonic and a minor (respectively major) third. These triads need not be played in a single octave in this same order, they can also be transposed with some at the bottom and others at the top, in the same sequence. For example, changing the order of pitches in a major triad can give a minor third - dominant - higher tonic (octave) which is called the first inversion of the major triad, and dominant - higher tonic - higher minor third, the second inversion. These triads can be formed based on relations from any pitch, and this base pitch is called the root of the triad. That is, a major/minor triad is a root - major/minor third - dominant in some transposition. In these triads there is one major third and one minor third interval.  Taking both intervals to be of major thirds, gives an augmented triad, which is actually a root - major third - minor sixth, and similarly, taking both intervals to be of minor thirds, gives a diminished triad, which is a root - minor third - tritone. These give some interesting dissonances which then resolve into consonances. Any triad or even any chord can be recognised by its root pitch. There are also suspended chords, with tonic - major second - fifth (second suspended chord) and tonic - perfect fourth - fifth (fourth suspended chord), which also have interesting dissonances that usually resolve into consonances. In a major key, the tonic, fourth and fifth give major triads, while the second, third and sixth give minor triads, while the seventh gives a diminished triad, diatonically. In a minor key, the tonic, fourth and fifth give minor triads, while the third, sixth and seventh give major triads and the second gives a diminished triad, diatonically. When scale degrees are raised to give harmonic and melodic minor scales from natural minor scales, the corresponding changes in key give a minor triad for the second, an augmented triad for the third, major triads for the fourth and fifth, and diminished triads for the sixth and seventh, each of these based on raised scale degrees.

The reference in harmonic tonality is given by the tonic triad, major or minor. The emphasised harmonic relations are in consonance with this tonic chord, and the de - emphasised dissonant harmonic relations give temporary unstable tension and movement which then resolves to stable consonances. This emphasis and de - emphasis of chords makes the tonic chord prominent and gives harmonic tonality (since the relation is between chords). Playing with a fixed tonic chord, is called playing in a key beginning at the root pitch of the tonic, in music using harmony. By the implied harmonic relations in the key, harmonic relations of chords with roots at different scale degrees are fixed. Chords have a hierarchy based on their functions relative to the most stable one, the tonic. The tonic function is the most stable, shown by chords based on the tonic pitch, the basis of a key. This function may be extended with chords based on pitches consonant to the tonic, which then share pitches with the tonic chord, and these are called tonic prolongations, based on the third and sixth degrees. Less stable than these is the dominant function, shown by chords based on the dominant/fifth or seventh/leading tone, and these give instability which is strongly resolved by moving to the tonic. Less stable than all of these is the pre - dominant function, with various less stable chords, including those based on the second and fourth, borrowed chords by tonicisation of non - tonic scale degrees, some altered chords as exemplified below, and almost innumerable possibilities. The pre - dominant function may resolve first to the dominant then the tonic, or directly to the tonic. A particular progression of harmonies, or a chord progression, defining the most direct hierarchy of these functions is tonic - pre - dominant - dominant - tonic, where a tonic prolongation may appear anywhere near the tonic. Within each function many different chords are possible, in different inversions. The order of chords, or chor progression may also be different but outlining some tension and resolution, and different from the progression described above. The resolution from dominant to tonic is the strongest and gives the most stable ending, or cadence, as described further, below. 

A chord can be bigger than a triad, having more than 3 distinct pitches (the same pitch in different octaves does not give distinct pitch values), and this can be done by extending the relations of thirds, from the fifth to seventh, ninth, eleventh scale degrees, etc. For example, in seventh chords, using different major and minor third interval relations between the root, third, fifth and seventh scale degrees can give major, dominant, minor major seventh, minor seventh, diminished, augmented, half diminished and augmented major seventh chords. The main limit on the number of pitches in a chord is basically that those pitches should be effectively heard by the listener. When there are many layers of sharply pitched music playing harmonically, each layer may not play a different scale degree, the scale degrees played by two different layers may be the same, possibly transposed to different octaves. For example, there may be 4 layers of music, or 4 voices, playing a triad, with 2 of the voices playing the same scale degree in the same or different octaves, since the number of distinct scale degrees in a triad is 3. This is called doubling of a pitch. In a chord, any notes may also be nearby, around the same octave, giving a closed position, or in far away positions by transposing octaves, in open positions. Such different harmonic arrangements between sharply pitched layers of music are called voicing. 

In a chord when there are clear harmonic relations, some pitches may even be omitted, especially in chords with many pitches, and because of the implied relations, this does not disturb harmony. Sometimes, certain pitches of a triad may be replaced with other pitches, like in suspended chords, where the third is replaced by a lower major second or higher perfect fourth. Pitches may also be added to give added chords. Such different combinations of pitches used to form chords, give different possible harmonic relations. Chords may not be played as such, as a group of simultaneously sounding pitches, and instead its constituent pitches may be played in order one after the other, forming arpeggios, or broken chords. This process is called arpeggiation, and although less harmonic in the sense that pitches are not playing simultaneously, the pitch relations are still harmonically based, so it is still completely a part of harmonic tonality. A sequence of chords used (and possibly repeated, varied or changed) is called a chord progression. The movements from and to different chords decide the actual movements between pitches used in harmonic music, and each line in it. The actual kinds of movements allowed depend on the particular system of music.

In harmonic tonality, cadences or endings of phrases, movements and pieces of music (please see the previous post for musical structure) are reached by resolving tensions to stable chords. They are defined by the chord progressions which make them up. Within short periods of music like phrases, this is mainly resolving dissonances to consonances. For whole movements and musical pieces, by resolving to the tonic chord from a chord consonant to the tonic. Cadences and their relative stabilities are defined by their harmonic function, as tonic, tonic prolongation, dominant and pre - dominant, as described above. An authentic cadence has a movement from a dominant chord to a tonic chord, and is the most stable cadence, while a plagal cadence has a movement from a subdominant chord to a tonic chord, less stable than an authentic cadence. These are the only kinds of cadences used to end movements and musical pieces. An authentic cadence where both dominant and tonic chords are in root position, with the tonic root pitch at the highest voice of the tonic chord is called a perfect authentic cadence, and is the most stable form of an authentic cadence. When the highest voice of the tonic chord is not the root, or when both chords are not in root position, or if the dominant chord is replaced with a leading tone chord (diminished chord on seventh degree), the cadence is called an imperfect authentic cadence, because of being relatively less stable than the perfect authentic cadence. An evaded cadence is an imperfect authentic cadence going from the second inversion of a dominant chord to the first inversion of the tonic chord. Phrases and periods of music may have other kinds of full or partial endings or cadences, including deceptive and half cadences. In deceptive cadences, the ending is like a cadence but changes at the very end, thar is, the dominant chord goes to a non - tonic chord, usually the submediant (sixth degree) chord, less stable than the tonic chord, and is not fully a cadence. In half cadences, any chord moves to a dominant chord, which must be resolved to the tonic chord later. The overall tonality is given by ending a musical section or composition with a tonic chord, resolving to the tonic chord, which is the most stable consonance, and in general, using a perfect authentic cadence. 

Although other chromatic notes may be added while playing in these scales, they are still used lesser than the main notes of the scale, and mostly not with other pitches of the same scale degree, since this causes a lot of dissonance. The chords corresponding to these are called altered chords. Some examples are, the Neapolitan Six, a minor second - fourth - minor sixth triad often used in first inversion, and augmented sixth chords, with a tritone - minor sixth - tonic triad in first inversion, with the tonic, major second or minor third added. The allowed or used consonances and dissonances depends on the style of music. This is not followed in chromatic music, which is atonal (see below). Other chords may be used as chromatic additions for different movements, and since these are not themselves in the home key, they are called borrowed chords. Major and minor keys with the same arrangement of intervals in an octave (steps/tones and half steps/semitones), called key signature, are said to be relative major and minor to each other, and moving from one to another is a smooth way to change major or minor relation to the other, without changing key signature. Keys from the same root with major or minor relations are called parallel keys, or parallel major and minor keys to each other. Many minor chords may be borrowed into their parallel major keys, and the Picardy third is the tonic major chord borrowed into its parallel minor key. But in a piece of music, there may not be a single tonic, and one tonic fixed for some part of the music, may then change to another tonic in another part of the piece. This change of tonic, which is given by changing keys, is called modulation of keys. Modulation may be done to a related key, such as a relative or parallel key, which can give a coherent and smooth sound, so is commonly used. Harmonic modulation may be allowed, necessary or forbidden depending on the musical system. Some chords like the fifth/dominant and second may also be tonicised, or made tonics, with chords from their keys being borrowed. The fifth of the fifth chord, or the fifth/dominant chord in the key of the fifth/dominant, added to the tonic key, is a common example. Keys based on pitches differing by a fifth may be arranged in order, to give a circle of keys with gradual increases and decreases in accidentals, and this is called the circle of fifths. This ordering gives the most consistent movements from key to key, and hence is the most commonly used framework for modulation to different keys, using a subset of consecutive keys. 

Counterpoint is the interaction of different layers in harmony - about where different layers move, ascend, descend, and how they are related in harmony and rhythm. Each layer is equally significant in counterpoint and has a movement in accordance to rules of harmonic tonality (which may depend on the harmonic musical system), and all layers are combined to give certain chords. In counterpoint, each layer has to be beautiful and complete by itself and also the combination of the layers has to match beautifully. To maintain uniqueness of layers, the layers generally move in a way that is not parallel (parallel harmony) but rather in contrary directions, giving counterpoint. Many kinds of relations are possible with various numbers of layers, and the number of layers is mainly limited by the need to be heard clearly and distinctly by the listener, while combining beautifully. Some musical systems may use only pitches found in a scale, and this restriction may also be used to give different intervals resulting in different chords, when the pitches in the scale are not symmetric and parallel. There may also be unchanging layers of sharply pitched music, where pitches are held constant to give a reference, and these are called a drones or pedal tones, and these are often in consonant pitches like the tonic, dominant and subdominant.

Melodic tonality and modes

In contrast to harmonic tonality, melodic tonality is a horizontal relation, since it is based on the consonances and dissonances between the pitches used in a single line. The base or reference of melodic tonality is given by a single tonic pitch rather than a group of pitches. Some number of pitches are chosen to form a scale. In melodic tonality, any choice of notes (without leaving the gap between the tonic and dominant empty) is possible within a scale. Then various rules on using pitches in the scale are applied to the scale, giving what is called a musical mode. As a pitch space, any scale of semitones or even microtones can be used since dissonance is horizontal and does not give an unpleasant effect because they don't play simultaneously, unlike in harmonic tonality. But even here, only subsets of 5, 6 or 7 notes (giving pentatonic, hexatonic and heptatonic scales) are used, by grouping many semitones (and microtones when used) under a single scale degree. Generally only one pitch/inflection of a scale degree appears contiguously even in melodic tonality. The ascending and descending scales need not be the same. The pitch intervals in a scale, which may be different while ascending and descending, and their relation to the tonic, give various consonant and dissonant relations. Although some other chromatic notes may be added while playing these scales, they are used lesser than the main notes of the scale, and mostly not with other pitches of the same scale degree, to avoid too much dissonance. But this generally happens much more rigorously than in harmonic tonality, since here only horizontal relations define tonality, and breaking these rules during movement (which is horizontal) will blur the melodic tonality present. So music with melodic tonality is sometimes farther from chromatic music than harmonically tonal music, and in some styles rules of tonality can be comparitively stricter. 

The use of modes and melodic tonality is very common in Asia and Upper Africa, and also to an extent, North, Central and South America, Australia and parts of Southern Europe and the Caucasus. The melodic tonalities and modal rules used in classical systems of Asia and North Africa may be used as a reference, since they are the most influential (although there are stylistic differences between them). A mode has a fixed tonic, and this determines the actual key in a musical piece. The actual consonant and dissonant relations, which actually exist between all pitches of a scale, are determined by certain chosen pitches. There are some chosen prominent pitches from the scale which are emphasised, and generally consonant to each other, and the pitches dissonant to these are de - emphasised. There is a pitch in the scale or scale degree, that is to be emphasised most, and this is called the primary tonal centre. This may be different from the tonic, and in fact, if the tonic is dissonant with this (so also not equal), it will be relatively de - emphasised even though it will be used since it is the tonic and gives tonality. The primary tonal centre is the centre of emphasis in a melodic mode. The next most emphasised note is the secondary tonal centre, and it has a consonance of a fifth/dominant or fourth/subdominant with the tonal centre. These are the two most emphasised notes, and other than these, there are stopping notes, where phrases end, and these are thus the other emphasised notes, and are consonant with either the primary or the secondary tonal centre (their overtones/harmonics). The de - emphasised notes are the others, and depending on the number of notes in the scale, some scale degrees (out of 7) may be completely omitted. But not all pitches of the scale that are consonant with the primary or secondary tonal centre may be stopping notes. The rules for this depend on the musical system and convention for the mode. In many modal musical systems, even stronger rules may be found, in the form of conditions on permitted pitch patterns or sequences in a mode. For example, even if a mode uses 7 scale degrees, it may be forbidden to move directly between 2 consecutive pitches among these and then it would be compulsory to move in a more zig - zag manner. Not respecting these rules may be considered wrong and incompatible with the musical style according to the convention of some systems, and so the movement between pitches depends on the system of music in melodic tonality. But the tonic defining the key, is always a stopping note even if not consonant with the tonal centres and music with melodic tonality still has to end at the tonic pitch irrespective of which pitches are tonal centres in a mode.

The emphasised melodic relations are in consonance with the tonal centres, and the de - emphasised dissonant melodic relations give temporary unstable tension and movement which then resolves to stable consonances. This emphasis and de - emphasis of pitches makes the tonal centres prominent and gives melodic tonality (since the relation is between pitches). Played a scale with fixed tonal centres is called playing in a mode with the implied tonality. The primary and secondary tonal centres determine and imply possibilities for other tonal centres through consonance. The reference in melodic tonality is the tonic pitch, and although the focus is on the tonal centres, and also music moves and approaches them is different ways, the tonic is still reached in the end, from some nearby interval. The instability and tension given by moving to de - emphasised and dissonant pitches, is resolved by moving to emphasised, consonant tonal centres, and even more, the primary and secondary tonal centres, the primary one being most emphasised. This is true in smaller parts of a musical piece, but in a big portion like a movement or the whole musical piece, the tension of moving away from the tonic is resolved by reaching the tonic at the very end of the movement or piece. Depending on the consonant or dissonant relation between the tonic and tonal centres, the tonic may be otherwise emphasised but because of the dependence on this relation, not always. But the movement to the tonic at the end of bigger portions of music confirms the tonic and makes it identifiable. And even other than this, other parts of the musical piece have to sometimes reach the tonic, so that the key and tonality based on the tonic are not obscured. This is regardless of the tonal relations the tonic has with the tonal centres, and this defining special position of the tonic makes it prominent and determines melodic tonality.

In some musical systems, such as those from Western Asia (Persian/Iranian, Arabic, Turkish), scales may not be used as a whole, but rather some groups of adjacent pitches (Jins in Arabic, Dang in Persian) may be used in different parts of an octave, or even different octaves. When these are used in different octaves, the octaves are not performed equally and each part of the octave depends on a tone cluster, which may be different than those of other octave parts. These pitch clusters themselves have some rules of consonance and dissonance, emphasis and de - emphasis, and moving from a tonal cluster with a tonic to another tonal cluster with a different tonic gives a kind of modulation between tonics. The tonics higher than that of the first tonal cluster are often its dominant, but sometimes may be its subdominant or even major/minor third. All these tonics are tonal centres. The beginning tonic is the primary tonal centre and the modulated tonic is a secondary tonal centre. Modulation in general, is the movement from one tonic to another tonic fixed at a tonal centre, and its relation to different pitches of the scale highlighted by moving away from the relations of the first tonic. This kind of modulation is called modal modulation. For coherence and consistency, modulation based on common tonal clusters, or same pitch intervals may be used. There may be different rules on which pitch movements to use, how they are related to the tonic or tonics, and which consonances and dissonances hold where, how they affect emphasis and de - emphasis at different melodic tonalities. Emphasising some relations of consonance, dissonance and movement between pitches of a mode even in just a part of an octave, can identify a mode by its tonal centres and relations among them and with other pitches of the mode. There may be modes built on very similar scales or even the same scale, but these pitch relations distinguish them from each other, and may make them sound very different from each other in spite of using the same pitches in total.

Music with melodic tonality may have one or more layers of sharply pitched music. Each layer has pitches moving according to the melodic tonality. There may also be unchanging layers of sharply pitched music, where pitches are held constant to give a reference, and these are called a drones or pedal tones, and these are often in consonant pitches like the tonic, dominant and subdominant. This can give a reference to the pitch and key (tonic). Many layers of sharply pitched music may also perform a single line together in unison, that is the same single line in different octaves. The single line may also be played with different variations by different layers, but each following melodic tonality defined in the music, and mostly having octave relations between each other, even with different shifts in pitch while making variations. The variations and pitch movements of different layers are based on the same single line, and are separate and each independently expressing the fixed melodic tonality, but all interrelated as variations of the same single line, and not with each pitch in a layer corresponding to one of another layer. Melodic tonality is also not disjoint with harmonic tonality, but the main basis of tonality is given by only one of these. Just as scales, which have pitches with some tonal relations, affect harmonic tonality that is played using them, when some harmonic layers are combined in music with melodic tonality, they follow the melodic tonality. Melodic tonality may use parallel harmony, where a line played with a defined melodic tonality, is replicated parallely by a line that is uniformly at a distance of a fixed interval from the first line. In this case both the layers are the based on the same line but shifted by a fixed gap between them. One common arrangement has a line playing with a defined tonic pitch and associated melodic tonality of the piece, and all the pitches play simultaneously at a distance of a fifth or dominant in another layer. When such parallel harmony is added, it plays as an enhancement to the already existing layer that has melodic tonality itself, and follows the defined melodic tonality without changing it with any harmonic relations.

In melodic tonality, cadences or endings of phrases, movements and pieces of music (please see the previous post for musical structure) are reached by resolving tensions to stable pitches - tonal centres. They are defined by the pitch sequences which make them up, movements between tonal centres. Within short periods of music like phrases, this is mainly resolving either dissonances/de - emphasised pitches to consonances/emphasised tonal centres. For whole movements and musical pieces, by resolving to the tonic pitch from a pitch consonant to the tonic or even just near the tonic. In the end of a musical piece, as well as at the end of movements, the tonic pitch has to be reached, generally from a pitch adjacent to it in the scale or mode. Phrases and periods of music may have other kinds of endings or cadences, where any sequences of pitches in the mode move to a tonal centre, following the rules of the mode. The tonal centres have the stopping notes where each phrase or period ends, resolving from unstable pitches that are not tonal centres. In specific musical systems, there may be cadential pitch sequences among the rules defining a mode, and these then have to be followed. The exception is with the tonic since it defines the key of the music. A tonic can be at the end of any cadence. Even when the tonal centres are dissonant with the tonic pitch, since the tonality has to be indicated, at least some phrases have to end even in the middle of the piece at the tonic since the key should be clear to define tonality. As mentioned before, the end of the cadence of movements and musical pieces is always the tonic pitch regardless of what tonal relations it may have with the tonal centres of the mode or scale. This gives a basis for melodic tonality.


Although most music is tonal, harmonic or melodic, there is also some music which is not tonal. This is called atonal or chromatic music. The musical styles and compositions that have been made on this basis are broadly from more recent times, and because of the ambiguity of the tonic, have not strongly influenced mainstream music of any part of the world. In atonal music, the relations (harmonic or melodic) that may indicate a tonic are intentionally avoided, and all pitches used have equal prominence. Relations of consonance and dissonance are not respected or followed, and pitches may appear in any order. Various combinations and permutations of pitches that are theoretically possible have been used to generate atonal music, without basing these on any tonal relations. Random choices are sometimes made on which pitches the sharply pitched music should move to, based on probability and chance rather than tonal calculations. When done with the chromatic scale, this is called chromaticism. As mentioned before, since much of music, tonal music is not very chromatic, but instead uses smaller scales and sometimes extends them. Chromatic and atonal music don't follow this and instead use chromatic intervals without any limitations. These conditions of atonality and often randomness of usage of pitch, lead to a very unique kind of music, which is also very rare. These distinguish atonal music from all other music in the world.

Tonality and broadly pitched musical sounds 

Now music using broadly pitched sounds is not sharply pitched so it does not actually have tonality, but in fact, even this is tonal music because of some factors. As mentioned before, broadly pitched sounds are well defined and limited in some ways, just like pitches in a sharply pitched instrument, and the usage of broadly pitched sounds is also determined by their place in a phrase and pattern. There are actually some sounds that are basic and distinguished from other sounds by being used repeatedly and used to come to rests. In particular, in most broadly pitched instruments, resonant tone/middle and resonant bass sounds give basic sounds and many musical cells, phrases, movements and even whole pieces end with them. Cadences always end with these basic sounds. The resonant/legato articulation resolves the tension of short non - resonant sounds, and the middle/tone or bass pitches (depending on instrument) resolve the tension created by moving to pitches above or below them. The repeated reaching of these sounds after different movements makes them prominent and they become a reference to other sounds played. As mentioned before, a broadly pitched instrument is that which does not produce all main sounds sharply pitched, but could produced some number of (generally few) sharply pitched sounds with other sounds broadly pitched. Broadly pitched instruments are in fact generally sharply pitched so that their basic sound (resonant middle/tone or bass) matches the tonic of the sharply pitched instruments that may play with them. Even when there is no sharply pitched instrument, the basic sound is still tuned to a clear central or reference sound, and this gives the perception of a tonic in relation to which other sounds can be measured. Repeating these sounds, returning to them from others as a stable resolution, and ending musical parts with them makes them recognisable and gives an effect similar to tonality, and relation of other sounds to a tonic. So generally, music of broadly pitched sounds is also appropriate to be considered tonal.

In the next post, the various kinds of music and usage of musical sounds, and musical textures will be discussed. Please see it here.

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