Tuesday, January 9, 3500

Iraq (c. 3500 BC) - Bass - Harmonics - Quality

Iraq is a country in Western Asia spanning most of the northwestern end of the Zagros mountain range, the eastern part of the Syrian Desert and the northern part of the Arabian Desert.

[Iraq - The Passion of 1,001 Nights (inspired by collection of tales dating back c. AD 800-900)]

It shares borders with Kuwait and Saudi Arabia to the south, Jordan to the west, Syria to the northwest, Turkey to the north, and Iran to the east. It has a very narrow section of coastline at Umm Qasr on the Persian Gulf. There are two major flowing rivers: the Tigris and the Euphrates. These provide Iraq with agriculturally capable land and contrast with the desert landscape that covers most of Western Asia.

Iraq's rich history dates back to ancient Mesopotamia. The region between the Tigris and Euphrates rivers is identified as the cradle of civilization and the birthplace of writing.

The region of Iraq was historically known as Mesopotamia (Greek: "between the rivers"). It was home to the world's first known civilization, the Sumerian culture, followed by the Akkadian, Babylonian, and Assyrian cultures, whose influence extended into neighboring regions as early as 5000 BC. These civilizations produced some of the earliest writing and some of the first sciences, mathematics, laws and philosophies of the world; hence its common epithet, the "Cradle of Civilization."

Ancient Mesopotamia was settled and conquered by numerous ancient civilizations. Dates for events in ancient Mesopotamia are still controversial, and several different methods and standards of dating exist for the Chronology of the ancient Near East; therefore, all dates are only estimates.

Mesopotamia has been home to some of the oldest major civilizations, including the Sumerians, Akkadians, Babylonians, and Assyrians. Mesopotamia as a distinct and self-determining cultural region began with the rise of the first cities in southern Mesopotmia ca. 5300 BC, and ended with the Persian conquest in 539 BC.

The Fertile Crescent was inhabited with several distinct, flourishing cultures between the end of the last ice age (c. 10,000 BC) and the beginning of history. One of the oldest known Neolithic sites in Mesopotamia is Jarmo, settled around 7000 BC and broadly contemporary with Jericho (in the Levant) and Çatal Hüyük (in Anatolia). It as well as other early Neolithic sites, such as Samarra and Tell Halaf were in northern Mesopotamia; later settlements in southern Mesopotamia required complicated irrigation methods. The first of these was Eridu, settled during the Ubaid period culture by farmers who bought with them the Samarran culture from the north. This was followed by the Uruk period and the emergence of the Sumerians.

The Sumerians were firmly established in Mesopotamia by the middle of the 4th millennium BC, in the archaeological Uruk period, although scholars dispute when they arrived.

It is hard to tell where the Sumerians might have come from because the Sumerian language is a language isolate, unrelated to any other known language. Their mythology includes many references to the area of Mesopotamia but little clue regarding their place of origin, perhaps indicating that they had been there for a long time. The Sumerian language is identifiable from its initially logographic script which arose last half of the 4th millenium BC. Sumer is known as the Cradle of civilization.

By the 3rd millennium BC, these urban centers had developed into increasingly complex societies. Irrigation and other means of exploiting food sources were being used to amass large surpluses, huge building projects were being undertaken by rulers, and political organization was becoming evermore sophisticated.

Throughout the millennium , the various city-states Kish, Uruk, Ur and Lagash vied for power and gained hegemony at various times. Nippur and Ngirsu were important religious centers, as was Eridu at this point. This was also the time of Gilgamesh, a semi-historical king of Uruk, and the subject of the famous Epic of Gilgamesh.

It is during this period that the potter's wheel was developed into the vehicular- and mill wheel.

[Ruins of the Hanging Gardens of Babylon]

Babylon is a city of ancient Mesopotamia, the remains of which can be found in present-day Al Hillah, Babil Province, Iraq, about 85 kilometers (55 mi) south of Baghdad.

All that remains today of the ancient famed city of Babylon is a mound, or tell, of broken mud-brick buildings and debris in the fertile Mesopotamian plain between the Tigris and Euphrates rivers, in Iraq. Historical resources inform us that Babylon was in the beginning a small town that had sprung up by the beginning of the third millennium BC (the dawn of the dynasties). The town flourished and attained prominence and political repute with the rise of the first Babylonian dynasty.

In the Bible, Babylon appears as Babel, interpreted by Book of Genesis 11:9 to mean "confusion" (of languages), from the verb balbal, "to confuse."

The earliest source to mention Babylon may be a dated tablet of the reign of Sargon of Akkad (ca. 24th century). The so-called "Weidner Chronicle" states that it was Sargon himself who built Babylon "in front of Akkad." Another chronicle likewise states that Sargon "dug up the dirt of the pit of Babylon, and made a counterpart of Babylon next to Agade."


There are two other clefs used in music -- the C clef (used fairly rarely) and the F clef, both shown in early Gregorian chant forms above)

The F-clef was, until fairly recently, written as above.

[The names of the spaces and lines in bass clef -- the higher B is just below middle C]

When the F-clef is placed on the fourth line, it is called the "bass clef." This is the only F-clef used today, so that the terms "F-clef" and "bass clef" are often regarded as synonymous.

This clef is used for the cello, euphonium, double bass, bass guitar, bassoon, contrabassoon, trombone, tuba, and timpani; for the lower part of keyboard instruments like the piano, organ, marimba and harpsichord (of which the upper part is usually written in treble clef); and for the lowest notes of the horn; and the baritone and bass voices.

The mnemonics for bass clef spaces and lines are "all cows eat grass" (or fairly non-scientifically, "all cars eat gas" -- a lot of it, these days...) and "good boys do fine always" (or "good boys don't fool around"... or even...hm...something to do with animals....).

[Relationship between notes in Bass and Treble Clefs]

When the C-clef is placed in the middle of the staff, it is called the alto clef. The middle of what looks like the "three" indicates the position of middle C.

This clef (sometimes called the viola clef) is currently used for the viola, the viola da gamba, and the alto trombone.

Formerly, it was used for the alto voice and by instruments playing a middle part (oboes, recorders, etc.) It occasionally turns up in keyboard music to the present day (Brahms's Organ Chorales, John Cage's Dream for piano).

When the C-clef is placed such that its midsection is on the fourth line (from the bottom) of the staff, it is called the tenor clef.

This clef is used for the upper ranges of the bassoon, violoncello, euphonium, double bass, and trombone (which all use the bass clef in their lower and middle ranges, and in their extreme high ranges, the treble clef as well). Formerly, it was used by the tenor part in vocal music but its use has been largely supplanted either with an octave version of the treble clef when written alone or the bass clef when combined on one staff with the bass part.

In former days, the three clefs (G, C, and F) were placed at a variety of pitch levels -- mercifully, this practice has largely died out. A typical musican can get away with an active knowledge of treble and bass clefs (meaning memorized) and a passive knowledge of alto and tenor (that one can figure out the notes in a short time interval)


Pythagorean tuning is a system of musical tuning in which the frequency relationships of all intervals are based on the ratio 3:2. Its name comes from medieval texts which attribute its discovery to Pythagoras, but its use has been documented as long ago as 3500 B.C. in Babylonian texts.

It is the oldest way of tuning the 12-note chromatic scale and, as such, it is the basis for (although distinct from) many other methods of tuning, such as the common equal temperament. 53 equal temperament is closely related to Pythagorean tuning because it is extremely similar to a very extended Pythagorean cycle of fifths.

Pythagorean tuning is based on a stack of perfect fifths, each tuned in the ratio 3:2, the next simplest ratio after 2:1, which is the ratio of an octave. The two notes G and D, for example, are tuned so that their frequencies are in the ratio 3:2 -- if G is tuned to 200 Hz, then the D is tuned to 300 Hz. The A a fifth above that D is also tuned in the ratio 3:2 -- with the D at 300 Hz, this puts the A at 450 Hz, 9:4 above the original G. When describing tunings, it is usual to speak of all notes as being within an octave of each other, and as this A is over an octave above the original G, it is usual to halve its frequency to move it down an octave. Therefore, the A is tuned to 225 Hz, a 9:8 above the G. The E a 3:2 above that A is tuned to the ratio 27:16 and so on, until the starting note, G, is arrived at again.

In applying this tuning to the chromatic scale, however, a problem arises: no number of 3:2s will fit exactly into an octave. Because of this, the G arrived at after twelve fifths is about a quarter of a semitone sharper than the G used to begin the process. The table below (starting at E flat) illustrates this, showing the note name, the ratio above D, and the value in cents above the D for each note in the chromatic scale. The cent values of the same notes in equal temperament are also given for comparison (marked in the table below as "et-Cents").

In order to keep the ratios in this table relatively simple, fifths are tuned down from D as well as up. The first note in the circle of fifths given here is E flat (equivalent to D#), from which five perfect fifths are tuned before arriving at D, the nominal unison note.

Note Ratio Cents et-Cents Interval

Eb 256:243 90.22 100 minor second

Bb 128:81 792.18 800 minor sixth

F 32:27 294.13 300 minor third

C 16:9 996.09 1000 minor seventh

G 4:3 498.04 500 perfect fourth

D 1:1 0 0 unison

A 3:2 701.96 700 perfect fifth

E 9:8 203.91 200 major second

B 27:16 905.87 900 major sixth

F# 81:64 407.82 400 major third

C# 243:128 1109.78 1100 major seventh

G# 729:512 611.73 600 augmented fourth

[D#] [2187:2048] [113.69] [100] [augmented unison]

In equal temperament, and most other modern tunings of the chromatic scale, pairs of enharmonic notes such as E flat and D sharp are thought of as being the same note -- however, as the above table indicates, in Pythagorean tuning, they theoretically have different ratios, and are at a different frequency. This discrepancy, of about 23.5 cents, or one quarter of a semitone, is known as a Pythagorean comma.

To get around this problem, Pythagorean tuning uses the above 12 notes from E flat to G sharp shown above, and then places above the G sharp another E flat, starting the sequence again. This leaves the interval G#—Eb sounding badly out of tune, meaning that any music which combines those two notes is unplayable in this tuning. A very out of tune interval such as this one is known as a wolf interval. In the case of Pythagorean tuning, all the fifths are 701.96 cents wide, in the exact ratio 3:2, except the wolf fifth, which is only 678.49 cents wide, nearly a quarter of a semitone flatter.

If the notes G# and Eb need to be sounded together, the position of the wolf fifth can be changed (for example, the above table could run from A to E, making that the wolf interval instead of Eb to G#). However, there will always be one wolf fifth in Pythagorean tuning, making it impossible to play in all keys in tune.

Because of the wolf interval, this tuning is rarely used nowadays, although it is thought to have been widespread. In music which does not change key very often, or which is not very harmonically adventurous, the wolf interval is unlikely to be a problem, as not all the possible fifths will be heard in such pieces.

Because fifths in Pythagorean tuning are in the simple ratio of 3:2, they sound very "smooth" and consonant. The thirds, by contrast, which are in the relatively complex ratios of 81:64 (for major thirds) and 32:27 (for minor thirds), sound less smooth. For this reason, Pythagorean tuning is particularly well suited to music which treats fifths as consonances, and thirds as dissonances. In western classical music, this usually means music written prior to the 15th century. As thirds came to be treated as consonances, so meantone temperament, and particularly quarter comma meantone, which tunes thirds to the relatively simple ratio of 5:4, became more popular. However, meantone still has a wolf interval, so is not suitable for all music.


Unisons, fourths, and fifths may be perfect, augmented, or diminished.

0 steps = P1
1/2 step = m2
1 step = M2
1 1/2 steps = m3
2 steps = M3

A fourth that contains 2 1/2 steps is called a perfect fourth

2 1/2 steps = P4

An interval involving 3 steps can be called a tritone

3 steps = Tritone

(This "evil-sounding"/"unrestful"/dissonant" interval has been known as the "Diabolus in Musica"/"Devil in Music," which can be spelled as an augmented fourth [A4], when involving four letter names, or a diminished fifth [d5] when involving five)

A fifth that contains 3 1/2 steps is called a perfect fifth

3 1/2 steps = P5


The tritone (tri- or three and tone) is a musical interval that spans three whole tones. The tritone is the same as an augmented fourth, which in 12-tone equal temperament is enharmonic to a diminished fifth. It is often used as the main interval of dissonance in Western harmony, and is important in the study of musical harmony.

Writers often use the term tritone to mean specifically half of an octave from a given tone, without regard to what system of tuning it may belong to. Two tritones add up to six whole tones, which in meantone temperament is a diesis less than an octave, but in equal temperament, where the diesis is tempered out, it is equal to a perfect octave. A common symbol for tritone is TT. It is also sometimes called a tritonus, the name used in German.

The tritone occurs naturally between the 4th and 7th scale degrees of the major scale (for example, from F to B in the key of C major).

Compared to other commonly occurring intervals like the major second or the minor third, the augmented fourth and the diminished fifth (both two valid enharmonic interpretations of the tritone) are considered awkward intervals to sing. Western composers have traditionally avoided using it explicitly in their melody lines, often preferring to use passing tones or extra note skipping instead of using a direct leap of an augmented fourth or diminished fifth in their melodies. However, as time went by, composers have gradually used the tritone more and more in their music, disregarding its awkwardness and exploiting its expressiveness.

The tritone is a restless interval, classed as a dissonance in Western music from the early Middle Ages through the end of the common practice period. This interval was frequently avoided in medieval ecclesiastical singing because of its dissonant quality. The first explicit prohibition of it seems to occur with

"the development of Guido of Arezzo's Hexacordal system which made B flat a diatonic note, namely as the 4th degree of the hexachordal on F. From then until the end of Renaissance the tritone, nicknamed the "diabolus in musicā" was regarded as an unstable interval and rejected as a consonance,"

The name diabolus in musica ("the Devil in music") has been applied to the interval from at least the early 18th century. Georg Philipp Telemann in 1733 notes that "mi contra fa ... welches die alten den Satan in der Music nenneten" ("mi against fa, which the ancients called 'Satan in music'"), while Johann Mattheson in 1739 writes that the "alten Solmisatores dieses angenehme Intervall mi contra fa oder den Teufel in der Music genannt haben" ("older singers with solmization called this pleasant interval 'mi contra fa' or 'the devil in music'"). Although both of these authors cite the association with the devil as from the past, there are no known citations of this term from the Middle Ages, as is commonly asserted.

However Denis Arnold, in the referential The New Oxford Companion to Music, suggests that the nickname was already applied early in the medieval music itself:

"It seems first to have been designated as a 'dangerous' interval when Guido of Arezzo developed his system of hexachords and with the introduction of B flat as a diatonic note, at much the same time acquiring its nickname of 'Diabolus in Musica' ('the devil in music')."

Because of that original symbolic association with the devil and its avoidance, this interval came to be heard in Western cultural convention as suggesting an "evil" connotative meaning in music. Today the interval continues to suggest an "oppressive," "scary," or "evil" sound.

However, suggestions that singers were excommunicated or otherwise punished by the Church for invoking this interval are likewise fanciful. At any rate, avoidance of the interval for musical reasons has a long history, stretching back to the parallel organum of the Musica Enchiriadis.

In all these expressions, including the commonly cited "mi contra fa est diablous in musica", the "mi" and "fa" refer to notes from two adjacent hexachords. For instance, in the tritone B-F, B would be "mi", that is the third scale degree in the "hard" hexachord beginning on G, while F would be "fa", that is the fourth scale degree in the "natural" hexachord beginning on C.

Later in history with the rise of the Baroque and Classical music era, that interval came to be perfectly accepted, but yet was used in a specific controlled way, notably through the principle of the tension/release mechanism of the tonal system. In that system (which is the fundamental musical grammar of Baroque and Classical music), the tritone is one of the defining intervals of the dominant-seventh chord and two tritones separated by a minor third give the fully-diminished seventh chord its characteristic sound. In minor, the diminished triad (comprising two minor thirds which together add up to a tritone) appears on the second scale degree, and thus features prominently in the progression iio-V-i. Often, the inversion iio6 is used to move the tritone to the inner voices as this allows for stepwise motion in the bass to the dominant root. In three-part counterpoint, free use of the diminished triad in first inversion is permitted, as this eliminates the tritone relation to the bass.

It is only with the Romantic music and modern classical music that composers started to use it totally freely, without functional limitations notably in an expressive way to exploit the evil connotations which are culturally associated to it (e.g., Liszt's use of the tritone to suggest hell in his Dante Sonata). The tritone was also exploited heavily in that period as an interval of modulation for its ability to evoke a strong reaction by moving quickly to distantly related keys. Later on, in twelve-tone music, serialism, and other 20th century compositional idioms it came to be considered as a neutral interval.

In some analyses of the works of 20th century composers, the tritone plays an important structural role; perhaps the most noted is the axis system, proposed by Ernő Lendvai, in his analysis of the use of tonality in the music of Béla Bartók. Tritones play prominent roles in the music of George Crumb.

Antonio Vivaldi uses the tritone in the movement Gratias Agimus Tibi in the bass part for Gloria in Excelsis Deo.

The beginning of Act II in Beethoven's opera Fidelio, where the timpani are tuned a tritone apart, to A and E-flat, instead of the usual perfect fifths, to set the mood for the dark dungeon.

Liszt's Dante Sonata prominently utilizes tritones.

Saint-Saëns literally made the tritone "the Devil in music" in Danse Macabre. In it, the violin soloist uses scordatura, tuning the top string down a half step (from E to E-flat). This creates a tritone with the open A string, giving the sound of Death tuning his fiddle for the dance.
Rimsky-Korsakov uses the tritone in the opening theme of the first movement of Scheherazade (Bb to E) to depict the evil sultan.

The tritone plays a major role in Jean Sibelius's Symphony No. 3 in C Major, op. 52, and even more so in the dark and austere Symphony No. 4 in A minor, op. 63.

Claude Debussy's Ce qu'a vu le vent d'Ouest exploits tritones throughout the entire piece.

The tritone is the very foundational interval of the new harmonic language Alexander Scriabin developed in the latter half of his career, and dozens of his pieces from about Op. 30 onwards either use successive chords with roots a tritone apart, or use the tritone itself as a prominent interval in many chords. This tritone relationship evolved into a full substitute in this new language for the traditional tonic-dominant tonal relationship, to the extent that the tritone interval became a consonance in Scriabin's usage, not needing resolution.

Mars -- The Bringer of War, the first movement from Gustav Holst's suite The Planets, uses the tritone as an effect to describe the horrors of warfare.

Carl Ruggles’s Sun Treader uses the tritone prominently in its non-Schoenberian atonal polyphonic syntax, usually alternating either with the perfect fourth or fifth.

Alban Berg -- in Wozzeck: Act I, Scene 3 -- ends the interlude after Marie's lullaby with a bass tritone oscillation, altered from previous perfect fourths, to presage the return of her soon-to-be-cuckolded common-law husband.

The tritone of C and F-sharp is a prominent interval in Benjamin Britten's War Requiem, signifying the theme of conflict and reconciliation.

Tritones play prominent roles in the music of George Crumb, including the opening trombone trio glissandi in Echoes of Time and the River, the opening soprano ornamentation and closing drones of Ancient Voices of Children, the motivic structure of Night of the Electric Insects and Devil Music from Black Angels, the evocations of whales and Richard Strauss in Vox Balaenae, and the tritone transposition of Spiral Galaxy from Makrokosmos, Volume I.

Black Sabbath's guitarist Tony Iommi used a tritone as the entire basis for his song Black Sabbath. He plays a tritone exclusively until halfway through the song.

The introduction and the main riff for most of Metallica's Harvester of Sorrow gets its menacing sound from the tritone.

Nu metal band Korn uses tritone in great amount in its works especially on their first album Korn.

Thrash metal band Slayer's 1998 album is entitled Diabolus in Musica and the song Bitter Peace features the tritone.

The intro to the song Purple Haze by the Jimi Hendrix Experience uses a tritone in which Hendrix plays a B-flat octave while bassist Noel Redding plays an E octave.

The intro to the song YYZ by Rush uses the tritone C-F-sharp several times over before entering the main riff.

The intro to the song Last Entertainment by the Swiss technical Thrash Metal band Coroner uses an A-D-flat tritone.

The intro to the song Charlie by Red Hot Chili Peppers uses a series of tritones: F-B, B-F, B-flat-E, and E-B-flat.

Many King Crimson songs (for example, Red) make extensive use of tritones.

One of the intro riffs in the song As I Am by Dream Theater uses the C-F-sharp tritone.

Buckethead makes extensive use of tritones in his rapid solos to give them a "robotic" and "unnatural" feel.

Mr. Bungle frequently uses tritones inits music so much to the point that the double tritone chord was informally named the Mr. Bungle chord.

Primus makes frequent use of tritones throughout their music, one of the most notable ones being Jerry Was A Race Car Driver.

Marilyn Manson's song Beautiful People uses the tritone throughout all of the song.

Keith Emerson uses a tritone in the intro to Emerson, Lake & Palmer's The Barbarian.

Spanish band Mago de oz (Wizard of Oz) in their album Gaia II features the song Diabuls in musica as a way to invoke the devil to the real word; the tritone features in the song also.

West Side Story, the musical by Leonard Bernstein, uses the tritone throughout as part of a characteristic motif that appears almost everywhere in the music. For instance, it opens the song Maria, and becomes the bassline for Cool.

The theme to the Fox Television series The Simpsons features a tritone prominently throughout, most notably in the bassline.

[4200 Fu Hsi / 3500 Iraq / 2000 China]