Saturday, July 25, 2020

Musical sounds - 1 - Tuned and variably pitched sounds

Various basic aspects of musical sounds, their kinds and relations in different musical styles of the world. 

This is the first of a 3 part post on musical sounds in music, for the second 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.



Musical sounds:

Musical art is expressed through the medium of sound, as sounds played in different ways, with various numbers of silences between them (for rhythm and related concepts, please see the previous post). Of course, without musical sounds, there can be no music at all.

Musical sounds can be of two kinds in relation to pitch, or highness of sound - variably pitched or broadly pitched sounds, and tuned or pitched sounds. The main difference between these is their relation to pitch, and not necessarily any other factor. Since musical sounds may satisfy some basic conditions of pitch relations, or not, they can be either variably pitched or tuned but not both simultaneously. These are alternatives to playing musical sounds, and possibly different instruments suitable to play each kind of sound, may be used for each of these.

Variably pitched sounds 

Musical sounds of variable pitch, means that the sounds have broadly varying pitch, and the pitches of the sounds don't or rather, may not have an exact relationship between them. The sounds are not of calculated, graduated pitch, but rather of different ranges of pitch, which may be described as low, middle, and high, etc. The important fact about variably pitched musical sounds is that they are not meant to project exact pitch relations when played. The sounds are generally of varying pitch, which can be identified as relatively higher or lower, by just hearing them, and are of beautiful quality and timbre, and so important by themselves even apart from the patterns they make, or the rhythms they follow. 
For such instruments, not making sounds of exactly related pitches is actually desirable and required, and not a compromise of the wish to make specificially tuned sounds. The particular sounds produced in such instruments are intentionally of variable pitches and should be appreciated for the effect of broadly varying pitch by itself, different from the effect of exactly related variation in pitches found in tuned instruments. Reversing this relation with pitches is often undesirable in such instruments since the instruments are made with preplanning, to produce the wanted kinds of sounds with respect to pitch. But the sounds are not completely random in pitch and have limited pitch range, and like in tuned instruments, these few pitches make up all sounds. Each sound in a variably pitched instrument is intended to be produced in a particular way with factors that define the sound (the factors are explained below). Flouting these defining factors is undesirable and may be considered wrong or ugly since then the sound becomes unidentified and somewhat random. The defined sounds in the instrument depend on both the natural structure of the instrument, as well as conventions of playing it. In tuned instruments, the difference is that, since there are particular pitch relations followed by the pitches of their musical sounds, disrupting them would defy some basic rules followed by pitches, and stick out like a blemish. This would sound ugly or undesirable, and so be out of tune, and hence be considered wrong. So for any instrument, variably pitched or tuned, the musical sounds produced by it are well defined and can be described with respect to how different factors influence it.

But also, it is often true that in variably pitched instruments, differences in pitch, articulation and sound length, accents and dynamics, as well as possible change of 'heaviness' (or thickness) of sound because of the way of playing, all contribute to the sound produced. When there is no specific relation of tuning between the pitches of the sounds, pitch does not precede the other factors described above that make sound, and the sound produced changes by varied combinations of these factors equally affecting it, rather than pitch taking some precedence. Of course, even in tuned instruments, which are tuned to sounds have pitches of specific relations, the other factors affect the sound as much, but because of the exact pitch relations, pitch can be individually identified as a more independent factor compared to variably pitched instruments. This is because, in many variably pitched instruments, the combined effect of all these factors may often have an effect on the timbre or tone colour of the sound, and even with some of these factors being the same, just changing the other factors in a sound can make a sound that is distinct from the first. In tuned instruments, since pitch relations are in fact independent of the other factors, they are not directly affected by changing the other factors, and identification of pitches is not affected much by the possible changes in timbre because of changing other factors.

The sounds may be descibed with respect to the factors of pitch, articulation and sound length, accents and dynamics, and heaviness, that make them up, in the following ways:

1. Pitch - Low/Bass, Middle (sometimes called Tone) and High/Treble (sometimes called Slap) pitch ranges can generally be used as criteria, but the actual number of pitches depends on the musical instrument producing them, and may be less than these 3 ranges, or even more, giving some variations within each range. Sometimes sounds may not have a single pitch but a glide or slide from one pitch to another, known as a continuous glissando or portamento. When this is stepwise this gives a stepwise glissando. But because of the kind of music played by variably pitched sounds (explained in the next part below), such glides are much lesser than discrete, singly pitched sounds. When sounds of different pitches are played simultaneously, this results in a combined sound with a group of pitches, different from but made of the singly pitched sounds that are played simultaneously. Some middle (or low) pitch of a sound may be fixed in relation to which the pitches of other sounds can be clearly described.

2. Articulation and sound length or resonance - Short and long sounds (sounds that resonate or sustain for short and long times), and staccato or non resonant sounds and legato or resonant sounds. Non resonant and resonant sounds are called closed and open sounds respectively too, because in some instruments the striking part actually closes and bounces from the surface of the instrument, to let sound resonate or not.

3. Accents and dynamics - In general accenting or emphasising sounds can be done in many ways (please see the previous post), but dynamics and resulting accents are basically loudness. Sounds can be comparitively soft or loud. Although this factor is not directly related to the others, it may sometimes affect timbre and even pitch, where in some instruments, accented or forceful louder strokes may raise the pitch of the sound produced. 

4. Heaviness - The sounds may be relatively heavy or light depending on how they are played. This could depend on the direction of stroking the instrument to produce sound, what is actually used to strike the instrument, and how many sounds are played simultaneously. If the instrument is stroked in a natural direction of force, such as nearer to the player, the sound will probably be heavier than that in the opposite direction. If the instrument is stroked by a comparitively big striker or big part of the striker, the sound will probably be heavier than that by a smaller striker or smaller part of the striker. Combining more than one single pitches as described above, also makes a heavier sound than a singly pitched sound. 

From the above factors, sounds could be generally defined as - resonant bass sound, nonresonant bass sound, resonant middle/tone sound, nonresonant middle/tone sound, resonant treble sound, and nonresonant treble sound, with possible variations of heaviness and even pitches within each of the pitch ranges, and combined sounds. A glissando may also be found between two of these ranges. These sounds may be described by these factors or using onomatopoeia, or imitative sounds, as short names for the sounds produced. Instruments producing variably pitched sounds may not necessarily have all sounds unrelated to the pitch relations in tuned instruments. Some of these sounds may be tuned indicating pitch relations (explained under tuned instruments) but all the sounds are not interrelated by such pitch relations so the whole space of sounds is variably pitched, because of not having complete relations of tuned sounds. But the main difference is that, a sound can be either variably pitched in an environment or space of sounds or tuned, but not simultaneously both. So, if an instruments does not make mainly tuned sounds, it will be considered variably pitched because of not indicating enough pitch relations to make a tuned sound space. Spaces with all sounds variably pitched, and some sounds variably pitched and some tuned, bring very beautiful sound movements.

The way in which pitch is varied depends on the instrument. Some of the common ways are:

1. Variably pitched drums: For non - uniformly tuned drums, that is, which have pitch variation over the surface of the drum head, pitch usually varies as lowest in the middle, to highest at the rim of the head (along the radius). The difference between these extreme pitches depends on the particular instrument, and to an extent, even the number of identified pitches played within this range. More than one sounds of single pitch can be combined by playing many strikes simultaneously, like striking more than one drum head (in the same or different instruments), to give a sound of combined pitch. Glissandos can be played by dragging or sliding the striker along the surface.

2. Paired cymbals, clappers, variably pitched struck gongs, shakers, scrapers, jingles and bells - In these instruments mostly two sounds are produced, a higher and a lower sound. Higher sounds are produced at the rims of cymbals and gongs, and raised (from striking) clappers, shakers, jingles and bells, while lower sounds are produced at the middle of cymbals and gongs, and lowered (struck down) clappers, shakers, jingles and bells. Scrapers may have increased pitch change as they are scraped forward and conversely, decrease pitch change while scraped backwards.

3. Jaw harps - The pitch is varied by changing the shape of the mouth (which the frame is kept against) and the amount of air filled within it, and sometimes even the opening of the throat. In general, as a natural property of sound, each pitch has certain related pitches called overtones (further explained below) and these can be played using such variations described above. 

4. Musical bows - Pitch varies along the length of the string of the musical bow, and if resonated by mouth, pitch can be changed as in the jaw harps.

5. Slit drums - These have pitch variation between the middle and rim like in drum heads, but also have holes or slits at different places, which when struck, give different pitches.

Tuned sounds

In tuned instruments, sounds are tuned to pitches that are calculated according to certain relations between them. As explained above, the main way tuned instruments differ from variably pitches instruments is that, since there are particular pitch relations followed by the pitches of their musical sounds, disrupting them would defy some basic rules followed by pitches, and stick out like a blemish. This would sound ugly or undesirable, and so be out of tune, and hence be considered wrong. 

Also, in tuned instruments, which are tuned to sounds have pitches of specific relations, even though the other factors (articulation and sound length, accents and dynamics, heaviness) affect the sound as much, because of the exact pitch relations, pitch can be individually identified as a more independent factor compared to variably pitched instruments. Since pitch relations are in fact independent of the other factors, they are not directly affected by changing the other factors, and identifying pitches is not affected much by the possible changes in timbre because of changing other factors.

Octave

A sound with a particular pitch, is related to sounds that have pitches, that are 2 - multiples of this pitch value. That is, for a given pitch of some value x, pitches of values 2x, 4x, 8x, etc. (powers of 2 times x) and even x/2, x/4, x/8, etc. (negative or inverse powers of 2 times x) are all specially related to the first sound. This relation makes all these sounds sound the same, but still actually higher or lower, like a single sound has been shifted to another level, but is still the same. This basic sameness that is a natural property of pitch, makes all sounds within the distance between any 2 such consecutive sounds (eg. distance between x and 2x, or x/2 and x/4), a single interval that can be copied at different pitch levels. This interval for any given pitch x, between x and 2x, is called an octave, and x is included in this octave (so 2x is in the next, higher octave). All the same pitches as described above, in different octaves, are in unison with each of these (same) pitches. 

Scale and scale degrees 

To fix a reference within each octave, a certain pitch is fixed, and called the tonic, or first scale degree. All the other pitches which may be used in an octave can be described in relation to this tonic pitch. The set of pitches within an octave are fixed, and called a scale. These pitches are repeated in all octaves. The relation of these pitches in the scale, to the tonic, are called scale degrees. The pitch that is a multiple of the tonic exactly between the tonic and higher tonic/unison (precisely (2)^(1/2) times the tonic pitch), is called the dominant, and also has a convergent relation with the tonic. This may be called the fifth scale degree. This makes it sound like it is meeting with the tonic, while still being different, just more different from the unisons of the tonic. Similarly, other scale degrees may be found, which could be called supertonic (second), mediant (third), subdominant (fourth), submediant (sixth), leading tone (seventh), while the dominant is the fifth scale degree, and tonic the first. 

These scale degrees may be labelled by different letters, or even onomatopoeia, or imitative sounds, for short form, and this is called solmisation. Some common solmisation systems are:
1. In Western solfege (sounds used in solmisation) system, the first to seventh scale degrees are called Do, Re, Mi, Fa, Sol, La, Ti/Si respectively. The solfege system used in Byzantine music, Paralaggi, has Pa, Vu, Ga, Di, Ke, Zo, Ni for first to seventh scale degrees respectively. In Canntaireachd system of Scottish Ceol Mor music, In/En/Em, A, O, D/H, I, Ie, U are used for first to seventh scale degrees respectively.
2. In North Indian Sargam/Swar system, the first to seventh scale degrees are called Saa, Re, Ga, Ma, Pa, Dha, Ni respectively, short forms for Shadj, Rishabh, Gandhar, Madhyam, Pancham, Dhaiwat, Nishad. In the South Indian solfege system these are Sa, Ri, Ga, Ma, Pa, Dha, Ni.
3. In Chinese Gongche system, first to seventh degrees are Siong/Shang, Cei/Che, Gong, Huan/Fan, Liu/He, Wu/Si, Yik/Yi respectively, although numbers 1 - 7 for scale degrees are commonly used, called .
4. In Korean Jeongganbo system, first to seventh scale degrees are Hwang, Tae, Go, Joong, Im, Nam, Ung respectively.
5. In Japanese solfege system, first to seventh scale degrees are I, Ro, Ha, Ni, Ho, He, To or for the Shakuhachi flute, Fu, Ho, U, E, Ya, I for six scale degrees. In Kunkunshi system, first to seventh scale degrees are Ai/Ko, Otsu/Go, Ro/Roku, Shitaro/Shi/Shichi, Jo/Hachi, Chu/Kyu, Shaku respectively.
6. In Burmese solfege system of Myanmar, first to seventh scale degrees are Duraka, Ryidawpyan, Myin Saing, Pale, Aukpyan, Chauk Thwe Nyunt, Hnyin Lone or Than Man, Hkunathan Gyi, Chauk Pauk, Nga Bauk, Leibauk, Thoun Bauk, Hnit Pauk respectively.
7. In Thai Thang system, the first to seventh scale degrees are Thang Nai, Thang Klang/Thang Luk Ot, Thang Phiang O Bon, Thang Kruat/Thang Nok, Thang Klang Haep, Thang Chawa, Thang Phiang O Lang/Thang Nai Lot respectively.
8. In Indonesian Gamelan system, the first to seventh scale degrees are Ji, Ro, Lu, Pat, Ma, Nem, Pi, which are short for number words Siji, Loro, Telu, Papat, Lima, Enem, Pitu (1 - 7 in Javanese).
9. In Iranian Dastgah system, the first to seventh scale degrees are Rast, Duka, Sika, Jaharka, Nawa, Hussaini, Auj, Qurdan respectively.
10.  In Turkish Makam and Arabic Durr I Mufassal Maqam systems , the first to seventh scale degrees may be called either Dal, Ra, Mim, Fa, Sad, Lam, Ta or by Persian names, in Arabic, and Koma/Fazla, Eksik Bakiye, Bakiye, Kuecuek Muecenneb, Bueyuek Muecenneb, Tanini, Artik Ikili in Turkish.

The exact pitches of the scale degrees among these notes depend on the musical system, but the chromatic scale used in the standard Western music system is a good reference, and other tunings may be described in relation to this. Since this is also very influential and has affected other tunings (which sometimes used to be more different), this is particularly useful in music. The chromatic scale is based on the division of an octave into 12 approximately equal parts. Each of these are called semitones or half steps, while the seven scale degrees mentioned before are whole tones or steps. Each scale degree (basically except the tonic and dominant which are fixed) has more than one inflection, major and minor, which are half steps/semitones grouped into a single degree. The major or sharp inflection is higher than the minor or flat inflection. Every semitone can be referred to as an augmented degree of one tone lower, or a diminished degree of one tone higher.

So, we get that the chromatic scale has these pitches in an octave: tonic/first, minor second, major second, minor third, major third, fourth, tritone, fifth, minor sixth, major sixth, minor seventh and major seventh. In solfege these may be called Do, Ra/Di, Re, Me/Ma/Ri, Mi, Fa, Fi/Se, Sol, Le/Lo/Si, La, Te/Ta/Li, Ti respectively. 

Any pitch that is of smaller interval than a semitone is called a microtone. Microtones may be used in some systems of music which use tunings different from the chromatic scale (12 almost equal parts of an octave). Many musical systems of West Asia (including Arabic, Turkish and Iranian Persian regions, and also a few southern regions of Central Asia) use 24 almost equal parts of an octave as a basis, and these are called quartertones, and are often clearly distinguished from semitones. Indian classical music systems (Northern and Southern systems are different in tuning) use microtones based on 24 or 22 almost equal parts of an octave, but the microtones are actually very close to semitones. The lower inflections are called Komal (flat) and Atikomal in North Indian classical music, and Flat and Koron in Iranian classical music, and higher inflections are called Teewr (sharp) and Teewrtar in North Indian classical music, and Sharp and Sori in Iranian classical music. Chinese, Korean, Japanese and Vietnamese music use the chromatic scale as a basis, but some styles of music have even used a tuning of around 7 equal parts of an octave. Thai, Lao, Khmer and West Central African music systems use a tuning of 7 almost equal parts of an octave. Tunings of 5 and 9 almost equal parts of an octave are used in Indonesian and Malaysian systems, and also in some Sub Saharan African systems. These tunings can also be approached by shifting semitones from the chromatic scale to match the other tunings.

In a scale there can be any number of notes, but generally there are 5, 6 or 7 notes (5 and 7 note scales are most common), since these are both necessary and sufficient to give a clear identifiable sound to the scale, since they don't have very big leaps and are also have far enough pitches. The scales formed by these are called pentatonic (5 notes), hexatonic (6 notes) and heptatonic (7 notes). The usage of scales and also number of notes in a scale depend completely on the musical style. Notes outside a scale may also be used in a musical piece, and for a 7 note (heptatonic) scale, would be chromatic addition of pitches, and is generally done in a limited way, although this may not be a strict rule in the whole of music (more explanation is below).

Consonance, dissonance and pitch organisation

Consonance and dissonance 

A sound has a certain identifiable pitch called its fundamental frequency, and also other pitches, which sound more quietly, called overtones or harmonics. The overtones/harmonics are convergent with the fundamental frequency and have some sameness with it, more or less than that between a tonic pitch and dominant pitch. As we may guess, for a given tonic pitch, its dominant pitch and also all unisons (octaves) of the tonic are among these overtones. This sameness between pitches is called consonance. It is also natural, and in fact true, that the most consonant pitches are unisons, or the same pitch in different octaves, and the next most consonant pair of pitches are a tonic and its dominant. As a sound resonates and fades, its fundamental frequency, the main pitch and others, the overtones merge and sound like the same, giving consonance. If one sound with a fundamental frequency, say a is played, and another sound with fundamental frequency b, which is actually an overtone of the first sound, are played together, they will have sameness in sound. That is, they will sound consonant and harmonious with each other. Since the overtones are, for a fact, more than one, the number of possible consonant pitch relations, is also more than one. The relation between two pitches that do not have this sameness, is dissonance. When two such pitches are played together, they sound different and possibly conflicting. The structures given to pitches other than octaves and choice of notes in a scale, depend on these consonances and dissonances. When a particular pitch is fixed as a reference, as mentioned before, this is called a tonic pitch. If played together with some pitches that are consonant with the tonic pitch, we will get a base group of pitches, or chord, the tonic chord. When music makes it clear that there is such a reference pitch or chord (group of pitches), a tonic, it is called tonal. Most music around the world is tonal, and displays relations of consonance and dissonance between pitches used. But it is possible for music to be atonal, or without a clear tonic pitch/chord, and it is discussed below, although such music is very rare and found only in some special styles.

The overtones or harmonics of a certain fixed pitch or tonic include, its octaves/unisons, dominant/fifth degree, subdominant/fourth degree, major third, minor third, major sixth and minor sixth and are consonant with the tonic. The other scale degrees (major and minor seconds, major and minor sevenths and tritone), are dissonant with the tonic. Any microtones which are not at some semitone based interval with the tonic are also dissonant with it, and are almost never played together with the tonic because the resulting dissonance is very unpleasant because of the very small interval between the pitches. Consonance is generally emphasised in tonal music and dissonance is used as a shift away from stable consonance, to bring interesting instability, which gives tension, and then returns to consonance, giving a stable resolution. 

The way in which pitch is varied depends on the instrument. Some of the common ways are:

1. Keyboards, tuned gongs, handpans, tuned drums and other tuned solids - these have different pieces or keys which are tuned to a fixed pitch and are struck to produce that pitch. Keys or pieces are arranged in a line or something similar, in order of increasing or sometimes decreasing pitch. Sounds of individual pitches may be produced or sounds of different pitches may be combined to give chords. Stepwise glissando is played by gliding stepwise from one pitch to another. Only discrete pitches are played. Different mediums may be used for resonance like strings, pipes, gourd resonators, etc. but regardless of this, these are all tuned percussion instruments.

2. Struck zithers/hammered dulcimers and harps/lyres - these have many different strings, each tuned to a different pitch, although groups of strings may be tuned to a single pitch to give a stronger sound. Longer strings have lower pitch and shorter strings have higher pitch, and these are arranged in order of increasing or decreasing pitch (from nearer to farther to the player). These are strummed, plucked or struck to produce particular pitches. Sounds of individual pitches may be produced or sounds of different pitches may be combined to give chords. Stepwise glissando is played by gliding stepwise from one pitch to another. Mainly discrete pitches are played, but some harps/lyres may be played by sliding on a single string to bend pitch and glide from one pitch to another. 

3. Strummed or plucked lutes - There are a few strings with lengthwise tuning, that is pitch is varied along the length each string, with lower pitches at longer part string lengths and higher pitches at shorter part string lengths, and different pitches may be marked along the string by bars called frets, and pressing a string on a fret gives the corresponding pitched sound, called fretting. Chords may be played by fretting or pressing different strings at different pitches of the chord, and stepwise glissandos can be played by stepwise sliding. In fretted instruments (instruments with frets) continuous glissandos/portamentos and pitch bending are played by bending a string along the fret to glide from the marked pitch to another. This may be played even by sliding along the length of the string, although this is more common in fretless instruments. Many discrete pitches and some slides may be played.

4. Strummed or plucked zithers - These may have two kinds of tunings, either similar to struck zithers and harps, where there are many strings, each tuned to a different pitch, or similar to strummed and plucked lutes, where only a few strings are used and pitch is varied along their length. For the first kind of tuning which is stringwise, playing is similar to harps and single pitches, chords, glissandos and portamentos, both stepwise and continuous, may be played. For the second kind of tuning which is lengthwise, pitch is varied along each string, playing sounds of single pitches, chords and discrete and continuous glissandos is similar to strummed and plucked lutes. Many discrete pitches and some slides may be played.

5. Bowed string instruments, hurdy gurdies - These have a few strings tuned lengthwise like strummed and plucked lutes, with pitch varying along the length of the string, with lower pitches at longer part string lengths and higher pitches at shorter part string lengths, and different pitches may be marked along the string by bars called frets, and pressing a string on a fret gives the corresponding pitched sound, called fretting. Although, these instruments are more commonly fretless than fretted. Single pitches and chords are played in bowed instruments similarly to strummed and plucked lutes, but hurdy gurdies mainly play single pitched sounds with constant pitches that are drones. Glissandos and pitch bending, both stepwise and continuous are played by sliding along the length of the string with stepwise marking for stepwise glissandos and smooth sliding for continuous glissandos. Since fretted instruments are less common, bending a string on a fret to bend pitch is also less common, and used only in fretted instruments. Sounds are played by bowing (rubbing a bow) on the strings in bowed instruments or turning a wheel to rub on the strings in hurdy gurdies. The length of such strokes can be anything a player wants and is able to play, and any number of pitches can be played within a single stroke. Both discrete pitches and slides may be played equally.

6. Mouth organs - These have different holes or pipes along a line or circle, tuned to different pitches, in increasing or decreasing order. Single pitches can be produced by blowing into single holes/pipes by inhaling or exhaling, controlling many pipes or blowing over many nearby holes can be used to play chords. Both stepwise and continuous glissandos can be performed by sliding stepwise between holes/pipes and slowly moving away and to holes/pipe holes. Many discrete pitches and some slides may be played.

7. Brass wind instruments - These have long tubes which are blown by applying pressure by lips, and changing pressure gives sounds of different (single) pitches that are harmonically related. Other pitches can be obtained by using valves and slides to change the length of the open tube. Stepwise and continuous glissandos may be played by moving stepwise to different pitches by changing pressure and length using valves and slides, and sliding between pitches continuously by continuously varying pressure or sliding valves and slides. But continuous slides are limited because of pressure needed to change pitch of the sounds. Many discrete pitches and some slides may be played.

8. Woodwind instruments - These have tubes which are blown into, with holes when closed and opened give different (single) pitched sounds. Change in pressure changes pitch too, and can be used to change octave. Changing pressure of blowing slowly or changing fingering of holes slowly can be used to play continuous glissandos. When stepwise movements are done fast, this gives stepwise glissandos. Both discrete pitches and slides may be played, but with smooth changes.


9. Singing voice - Pitch is changed in singing by the opening of the vocal cords in the throat of the singer. More open cords correspond to lower pitches while more closed cords give high pitches. Controlling this by sensation gives different (single) pitched sounds. Continuous glissandos, stepwise glissandos and pitch bendings are sung by sliding between two pitches by stepwise pausing or continuously changing the vocal cord opening. The human voice may have different registers at different pitch ranges - creaky voice (lowest), middle voice (middle) and falsetto (highest). Most singing is done using a middle voice but the other two registers may also be used sometimes, and they may be combined with the middle voice to give certain singing styles like throat singing (middle voice and creaky voice mixed) and yodeling (middle voice and falsetto mixed). Both discrete pitches and slides may be played, but with smooth changes.

In the next post, possible kinds of tonality and their features will be explained. Please see it here.

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