The Musical Origin of the Seven-Day Week

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[This is a guest post by Sara de Rose.]

Calendars, old and new, are based on astronomical cycles: the yearly cycle of the sun; the monthly cycle of the moon. But there is one unit of time that doesn’t adhere to any celestial rhythm: the seven-day week.

Celsus, a second century Greek philosopher, wrote that the week-day order is based on “musical reasons…quoted by the Persian theology.” 

Persia (Iran) was the neighbor of Mesopotamia (Iraq). Archaeological artifacts suggest that the two cultures shared the same musical system, and cuneiform tablets from Mesopotamia have allowed archaeologists to re-construct this system. The consensus is that, from at least 1800 BC, the Mesopotamians used a seven-note scale that is the ancestor of our modern major scale – and the structure of this scale was understood to be related to the sequence 4,1,5,2,6,3,7. 

Tablet CBS 1766 gives a visual representation of this system. On this tablet is drawn a seven-pointed star, with points numbered 1 to 7 and labelled with the names of the strings of the Mesopotamian lyre. By following the diagonals of the star, the sequence 4,1,5,2,6,3,7 is generated. In the table drawn below the star are written inversions of this sequence.

Before CBS 1766 was understood to relate to music in 2007, it was thought by archaeologists to be “an astrological scheme to relate the seven ancient planets to the seven days of the week,” and, in fact, the sequence 4,1,5,2,6,3,7 explains the week-day order. To see this, we must first understand how our ancestors pictured the universe – because the days of the week are named after the sun, the moon, and the five planets visible to the naked eye. Sunday is named after the sun; Monday, after the moon; Tuesday (French, Mardi), after Mars; Wednesday (French, Mercredi), after Mercury; Thursday (French, Jeudi), after Jupiter; Friday (French, Vendredi), after Venus; and Saturday after Saturn. 

To an observer on earth, these seven bodies all appear to travel through the constellations of the zodiac, which provide a backdrop against which their movements can be tracked. What the observer notices is that the sun, the moon, and the planets all appear to move at different speeds. 

The moon appears to move most quickly through the constellations, while Saturn appears to move most slowly. And although we know, today, that the earth circles the sun, what we actually experience – and what the Mesopotamians saw – is the illusion that the earth is stationary and that the sun moves through the constellations at the relative speed of the earth: slower than Venus (and Mercury and the moon) but faster than Mars (and Jupiter and Saturn). Arranging these bodies from fastest to slowest in orbits or “spheres” nestled around a central earth creates the model shown here. 

Notice that the days of the week are not arranged according to the speeds of the seven classical planets, as given by the ancient model of the universe. Instead, listing the sphere numbers of these bodies in their week-day order gives: Sunday, 4; Monday, 1; Tuesday, 5; Wednesday, 2; Thursday, 6; Friday, 3; and Saturday, 7 – the musical sequence 4,1,5,2,6,3,7. Cassius Dio, a Roman contemporary of Celsus, confirmed the musical origin of the week: “you will find all the days to be in a kind of musical connection with the arrangement of the heavens.” 

Now let’s look at how the sequence 4,1,5,2,6,3,7 is related to the major scale. To do this, we must introduce the “circle of fifths” – a circular arrangement of twelve notes that was known to the Mesopotamians, and is still used today to teach music. If we select the notes in a major scale from the circle of fifths, we generate the sequence 4,1,5,2,6,3,7. For example, the 1st note in the scale of C Major is C; the 2nd is D; the 3rd, E; the 4th, F; the 5th, G; the 6th, A; and the 7th, B. To find the notes in other major scales, we simply rotate the sequence 4,1,5,2,6,3,7 on the circle.

 To summarize, the days of the week are named after the seven classical planets and ordered using the musical sequence 4,1,5,2,6,3,7. But what is the deeper philosophical reason behind this?

Celsus – who, as we saw earlier, described the week-day order as based on “musical reasons…” – was documenting a ritual of the Mithraic Mysteries in which initiates climbed a ladder (Latin ‘scala’, the root of the musical term ‘scale’) of seven rungs, where each rung was associated with a classical planet, in the order 4,1,5,2,6,3,7. According to Celsus, this ladder represented of the journey of the soul through the planetary spheres.

Two hundred years after Celsus, Church Father Gregory of Nyssa described the week as having a spiritual function: to provide a means for the soul to ascend toward God. And not only did Nyssa believe that the individual undergoes this passage, he saw the entire history of the human race as a progression toward the divine — a process that he called “akolouthia,” a Greek term that translates as “sequence.”

Gregory may have known about the musical origin of the week, for he wrote: “we accept the law concerning the octave which cleanses and circumcises because once time represented by the number seven comes to a close, the octave succeeds it. This day is called the eighth because it follows the seventh … and is no longer subject to numerical succession.”

 The law of the octave became a central tenet of the Christian faith and gave rise to a definition of the word octave still found in most dictionaries: “a period of eight days beginning with the day of a Church festival.” Yet not only is the week defined as an ‘octave,’ the word ‘week’ itself can be traced to the German word ‘woche’, which comes from a base meaning “sequence, series.”

Each week we live through the musical sequence 4,1,5,2,6,3,7, a sequence that has been known to the human race for at least 4000 years. Over time, this sequence came to symbolize the ascent of the soul in widely different traditions: in Zoroastrianism, in Mithraism, in Christianity, and even in alchemical initiation. 

This is a shared cultural heritage of immense proportions, with the power to unite people of all traditions – for it comes down to us in an ancient and universal language: the language of music.

Selected readings


  1. martin schwartz said,

    May 6, 2022 @ 11:54 pm

    A pioneer in this kind of research is Joscelyn Godwin. I think Celsus
    got Mesopotamians, the relevant group, confused with Persians.

  2. maidhc said,

    May 7, 2022 @ 1:46 am

    In the circle of fifths 4,1,5,2,6,3,7 completing the cycle 7, 4 requires a diminished fifth rather than a perfect fifth. But doing things this way, you could put the diminished fifth between any two items of the sequence. Instead of C D E F G A B, you could just as well have C Db Eb F G Ab Bb (i.e., the Phrygian mode). This will generate all of what are called the Greek modes, including the rather peculiar Locrian. (We don't use the same names today as the ancient Greeks.)

    If the Babylonians tuned their lyres by tuning the strings in fifths with each other, allowing one diminished fifth, and assuming seven notes in a scale, they would get the Greek modes too. Or perhaps they should be called Babylonian modes.

    You can try to generate the chromatic scale using a cycle of fifths, and you will discover that the difference between twelve just perfect fifths and seven octaves is the Pythagorean comma (roughly a quarter of a semitone). Apparently this was done in ancient China. It's not clear to me how the Chinese dealt with the Pythagorean comma, but the paper is about 170 pages long, so it's a challenge to get at all the details.

    The problem of the Pythagorean comma was the great problem in European Renaissance music theory. We now deal with it mostly by distributing the comma equally around all the intervals in the chromatic scale (equal temperament).

    BTW, in the abridged paper all the heavy lifting is done by "It is the general
    consensus among music archaeologists". You have to read the non-abridged paper to get at the real details.

    The big question that occurs to me is that, if such a musical system existed unchanged over millennia, and was shared with all the cultures that were in contact with ancient Mesopotamia, all the way to China, why isn't it still in use today?

    Look at the huge variety of musical scales in use just in Europe, the Middle East and the subcontinent, most of which are not modal derivations of the major scale. Christian liturgical music developed out of Jewish liturgical music, which was at one time perhaps connected to this system. And this, in its descendant western European music, is where we see the greatest influence of the system today. (Setting aside the problem that the explanation does not extend well to the minor scale.)

    Nowadays you don't have to go too far east in Europe, to a line roughly through the Balkans, and you're in a different world.

    Another question: what about ancient Egypt?

  3. Robot Therapist said,

    May 7, 2022 @ 3:03 am


  4. Maxwell Martin said,

    May 7, 2022 @ 4:54 am

    The numbers (both on the star and in the two columns) seem to have been added by the author of this excellent analysis. Presumably they correspond to numbers on the cuneiform tablet, do they not?

  5. James said,

    May 7, 2022 @ 5:56 am

    Very interesting – can someone give an idea of whether this is generally known and accepted stuff, or whether it's a new proposal that is yet to be widely discussed and assessed?

  6. AntC said,

    May 7, 2022 @ 5:56 am

    The Hebrew Bible offers the explanation that God created the world in six days. The first day is then given the literal name First (in Hebrew: ראשון), the second being called Second (שני) and so forth for the first six days, …
    A continuous seven-day cycle that runs throughout history without reference to the phases of the moon was first practiced in Judaism, dated to the 6th century BC at the latest. … Babylonian calendar … the Jewish week was adopted from the Babylonians while removing the moon-dependency.

    The Hebrew bible is a lot older than Celsus. The Roman calendar was based on (Lunar) months, not weeks — that is, until they adopted Christianity using Hebrew weeks. (The 28-day months got corrupted by various Emperors poaching days; also by the dashed inconvenience of no astronomical cycles exactly fitting together.)

    But there is one unit of time that doesn’t adhere to any celestial rhythm: the seven-day week.

    The seven-day week fits (almost) into a 28-day lunar month. By "almost" I means no worse than the moon cycle actually being just over 28 days, and a year just over 13 moon cycles.

    Naming the days after Roman/Greek gods is post-Christianity/post-hoc mythologising.

  7. James said,

    May 7, 2022 @ 6:00 am

    I'm a bit confused by "The law of the octave became a central tenet of the Christian faith". What is this tenet?

  8. AntC said,

    May 7, 2022 @ 6:25 am

    Online etymology for Proto-Germanic *wikō(n)- -> English 'week'.

  9. AntC said,

    May 7, 2022 @ 7:19 am

    The consensus is that, from at least 1800 BC, the Mesopotamians used a seven-note scale that is the ancestor of our modern major scale …

    The Western scale is usually called "Pythagorean Tuning" — although it's doubtful Pythagoras had anything to do with it. That wiki thinks it more likely Eratosthenes, who pre-dates Celsus.

    Mesopotamian scale seems to be inconsistent with Pythagorean tuning:

    The Mesopotamians seem to have utilized a heptatonic Lydian scale, heptatonic meaning a scale with seven pitches. The Lydian scale is the regular major scale with a raised fourth.

    The Pythagorean scale derives from natural harmonics — apparent by overblowing a horn, or dividing a plucked string by whole-number intervals. The 'octave' is first harmonic (halve string length); the octave-plus-'fifth' is second harmonic (a third string length) aka Dominant. The 'fourth' aka Sub-Dominant is _not_ a natural harmonic, but is obtained "by moving the same ratio down" as the wiki puts it — that is by moving down a ration of 3:2 from the 'octave'. That is, the note you started with is a harmonic of the 'fourth'.

    The tonal difference (ratio) between 'fourth' and 'fifth' is what defines a tone. So you can't be using a "raised fourth": you'd have failed to fix a tone/you'd be clashing with natural harmonics.

    The 'circle of fifths' , as @maidhc says, is more of a mathematician's kludge: it needs small clashes against the natural harmonics, and couldn't really be implemented until well-tempering was understood (during Bach's time — the 48 Preludes and Fugues of 'The well-tempered clavier' is his exploiting the technology). "kludge" doesn't take away from the sheer bravura of the 48 — or of 'Giant Steps'.

    (I'm putting those interval ordinals in scare quotes, because they only come out in that sequence after you've shunted them up/down by octaves. And an 'octave' only comes out as eighth note after you've divided the first harmonic interval at the 'fourth' and 'fifth'; then divided the gaps into whole notes (two each) and discovered you get two half-tones — which is why there's no black key between E/F nor B/C on a piano. That placement gives the white notes playing a C Major scale. Other placements give other 'modes' Ionian, Dorian, … used more often in Renaissance music before Baroque regularised to Major/Minor.)

    I'm very doubtful the Mesopotamians understood the 'circle of fifths'. I think Ms de Rose is mixing up several anachronisms.

  10. David Marjanović said,

    May 7, 2022 @ 8:43 am

    'The well-tempered clavier'

    I know that's the established title in English, but I should point out that Klavier, as in Das wohltemperierte Klavier, is simply the German word for "piano".

  11. James said,

    May 7, 2022 @ 9:29 am

    I know that's the established title in English, but I should point out that Klavier, as in Das wohltemperierte Klavier, is simply the German word for "piano".

    At the time Das wohltemperierte Klavier was written, the piano was in its earliest infancy in Italy and was unknown in Germany. Klavier referred to any keyboard instrument, for example a harpsichord or a clavichord. That's why it's not usually translated as "piano" in that context.

  12. Maxwell Martin said,

    May 7, 2022 @ 9:40 am

    In the light of the post, it is easy to understand not only why the English nouns meaning 'Saturday' and 'Saturn' are related but also why the Hebrew ones having those two meanings are too: respectively שבת (shabat) and שבתאי (shabetay).

  13. Robert Coren said,

    May 7, 2022 @ 9:53 am

    @AntC: The 7-day week also almost fits into the 365-day year (leaving one extra day, alas).

  14. Kenny Easwaran said,

    May 7, 2022 @ 10:06 am

    AntC – the Lydian scale with raised fourth is actually a *better* fit to the explanation given here than a standard major scale. The sequence FGABCDEF precisely is a scale with a raised fourth. If you take the seven tones in a circle of fifths above F, and reduce them to the same octave, then you get precisely this Lydian scale.

    The modern major scale is the Ionian mode, which starts a fifth up from F, and needs to either have one of the tones a fifth down from the start rather than all of them being up, or have the seventh tone in the scale be a diminished fifth up rather than a perfect fifth.

  15. Gregory Kusnick said,

    May 7, 2022 @ 11:34 am

    According to Wikipedia, the sequence of weekday names derives from the ancient system of "planetary hours". Basically this involves assigning a planet to each hour of the day, starting with Saturn at 12:00 AM Saturday, and proceeding inward in celestial-sphere order (i.e. Saturn, Jupiter, Mars, Sun, Venus, Mercury, Moon). The 25th hour (i.e. the first hour of the next day) is the 4th hour of the third cycle of seven, hence the 7-4-1-5-2-6-3 ordering of weekday names.

    Any resemblance to the musical circle of fifths would (on this theory) seem to be coincidental.

  16. Coby L said,

    May 7, 2022 @ 11:51 am

    @David Marjanović:
    The usage of Klavier as "simply the German word for 'piano'" is relatively recent. To quote German Wikipedia, Klavier:

    Historisch bezeichnete Klavier, bis ins 19. Jahrhundert in der Schreibung Clavier oder Clavir, allgemein irgendein Tasteninstrument, gelegentlich auch nur eine Klaviatur, also einen Teil eines Instruments.

  17. David Marjanović said,

    May 7, 2022 @ 1:15 pm

    Oh! I had switched the lifetimes of Bach and Mozart in my head, it seems.

    Any resemblance to the musical circle of fifths would (on this theory) seem to be coincidental.

    That makes sense.

  18. Julian Hook said,

    May 7, 2022 @ 1:15 pm

    The post mentions that "CBS 1766 was understood to relate to music in 2007" but does not give the citation: Caroline Waerzeggers and Ronny Siebes, "An Alternative Interpretation of the Seven-Pointed Star on CBS 1766", Nouvelles assyriologiques brèves et utilitaires 20, no. 2 (2007), 43–45.

    For a somewhat more detailed account by a musicologist, see Leon Crickmore, "A Musical and Mathematical Context for CBS 1766," Music Theory Spectrum 30, no. 2 (2008), 327–338.

  19. Michèle Sharik Pituley said,

    May 7, 2022 @ 4:08 pm

    @maidhc: the rather peculiar Locrian

    I love the joke: Locrian is only a theoretical mode because it's got no soul*. :-)

    *sol — using Do as the tonic, Locrian mode is: do ra me fa sa le te do instead of the Ionian do re mi fa sol la ti do.

  20. AntC said,

    May 7, 2022 @ 6:17 pm

    Das wohltemperierte Klavier

    I thought David M was going to point out that Bach used "well-tempered", not "equal-tempered". There's a story about that on Youtube that even this Bach nerd found too dull:

    Bach used to tune his own household keyboards (Harpsichords, Spinets, Clavichords), and acted as consultant to organ-builders constructing well-tempered organs (not very tunable) for this new-fangled music. The video claims (with examples) the 48 are not aimed at an equal tuning, but rather a tuning that gives a 'brighter' tone to the bright pieces and a mournful tone to the subdued pieces.

    Furthermore the 48 would not be played all through as they are in concerts today. (Indeed probably they were never played in public.) Before the piano (which Bach was), keyboard instruments used to go out of tune overnight. So the claim is Bach would adjust the tuning before playing, according to which pieces he was about to play.

    If you can hear the difference between the same Fugue played in two different tunings, your ear (and patience) is better than mine.

  21. AntC said,

    May 7, 2022 @ 6:37 pm

    @Robert The 7-day week also almost fits into the 365-day year (leaving one extra day, alas).

    Yes, there's lots of "almost"s. But does anyone (ancient or modern) make use of: This year started on a Saturday, so next year on a Sunday?

    The Romans abandoned 13 lunar cycles almost fitting in a year; I guess because 13 is an awkward number to reckon with. Taking 12 months allows for dividing into four seasons; likewise 28 = 4 x 7 is more tractable.

    Then taking seven as the number to reason about [Lewis Carroll] Celsus/the Mithraists looked for seven occurring elsewhere. For example, the Classically-known planets. But that can be only coincidence: there are more than seven planets.

    @Gregory Any resemblance to the musical circle of fifths would (on this theory) seem to be coincidental.

    It's all coincidence: Mithraic mysticism; Numerology; Astrology; Seven Deadly Sins.

  22. AntC said,

    May 8, 2022 @ 12:23 am

    @Kenny the Lydian scale with raised fourth is actually a *better* fit to the explanation given here than a standard major scale. The sequence FGABCDEF precisely is a scale with a raised fourth.

    Thank you. Yes you're right. But then if we continue upwards by a natural harmonic 'fifth' from that B (i.e. a raised B♭), we get to F♯ (Pythagorean comma withstanding), not back to the fundamental note F. So the CBS 1766 tablet's line from 4 to 1 is bogus/much worse of a kludge than Pythagorean tuning.

    Also we don't need to go to that raised fourth to generate a Chinese pentatonic scale (the black notes on a keyboard) — Figure 40 of the paper.

    @maidhc the paper is about 170 pages long, so it's a challenge to get at all the details.

    Indeed. There's really two largely unconnected topics there — of which the 'Musico-Cosmologies' from p111 onwards — essentially itemising how various mysticists saw coincidences with sets of seven — significantly detracts from the serious musicology. Unfortunately that's the part mostly featured in this post.

    I'm surprised there's no mention in the post of the discovery of instruments in the Tarim basin that look very similar to Mesopotamian instruments.

  23. AntC said,

    May 8, 2022 @ 12:48 am

    So we have three similar tuning systems: Mesopotamian per tablet CBS 1766; Pythagorean/Western music; Chinese — a tradition dating from the Guo Yu (fifth century BC).

    Are they sufficiently similar that must be from cultural transmission?

    I think not: it's physics/harmony; plus some tricky work with ratios and exponentiation. We know all those cultures were mathematically savvy. Then it's not exactly coincidence, but independent discovery of underlying principles.

    From the paper, the instruments found in the Tarim basin seem to be in a stylistic dead end. They could plausibly have come from Mesopotamia/Near East. That style seems not to have travelled on to China.

    Disclaimer: I'm only a keen amateur, not a qualified musicologist/please consult a licensed professional. Was an actual musicologist asked to review the paper before publication in SPP?

  24. John Swindle said,

    May 8, 2022 @ 1:09 am

    Surely harpsichords and clavichords still go out of tune overnight, especially the ones homemade from kits, if that's still a thing. And still require the circle of fifths and a little fudging (or maybe an electronic pitchpipe, for some users), but not necessarily according to which piece you're going to attempt to play.

  25. Bob Ladd said,

    May 8, 2022 @ 3:15 am

    @David Marjanović,@James,@CobyL
    It seems a safe guess that the original meaning of Klavier in German was simply 'keyboard'. The word is French (clavier, related to clef 'key') and in French it still just means 'keyboard' and applies equally well to computer keyboards as to pianos and organs.

    The use of key in this sense, according to Kluge's German etymological dictionary, is metaphorical and based on organ technology: pressing a "key" opened the valve on the corresponding organ pipe. According to Kluge, the same metaphor originally worked in German as well (i.e. Schlüssel 'key' was used for the individual keys on an organ keyboard) but this was replaced in the 18th century by Taste, borrowed from Italian tasto. (That word is ultimately related to English taste by yet another etymological chain of metaphors, but we can stop here.)

  26. AntC said,

    May 8, 2022 @ 4:53 am

    Surely harpsichords and clavichords still go out of tune overnight,

    Yes, but not so much: central heating keeps them at a steady temperature; metal strings rather than gut; better quality framing that doesn't 'give' under tension.

    … according to which piece you're going to attempt to play.

    The argument in the video (don't shoot me I'm only the piano player) was that since Bach needed to tune the instrument every day, he might as well tune it differently for the day's programme.

    (How you could keep four harpsichords in tune with each other, in a drafty salon, for long enough to perform a concerto, is beyond me.

    In the middle movement, Bach has the four harpsichords playing differently-articulated arpeggios in a very unusual tonal blend,

    "unusual tonal" means out of tune? Quicksilver arpeggios so nobody notices. Sheer genius.)

  27. Sara de Rose said,

    May 8, 2022 @ 9:59 am

    I am Sara de Rose, the author of the original post. I’m glad that the post has generated so much discussion. Please let me respond to some of your comments.
    In response to James: This is ground breaking work. I encourage (no, implore) anyone with a critical mind to look at the very extensive evidence in my paper (Sara de Rose, "A Proposed Mesopotamian Origin for the Ancient Musical and Musico-Cosmological Systems of the West and China", Sino-Platonic Papers, 320 (December, 2021). What I hope for is a wide-ranging academic discussion that will bring this theory up for serious consideration. I know that academic papers are not for everyone, and to bridge this gap, I’ve created this short Youtube video, which basically duplicates the information contained in the original post. I ask that anyone interested in furthering this discussion watch the video and share it as widely as possible. Thank you. Video link: “The Musical Origin of the Seven-day Week”
    Also, in response to James: What is the law of the octave? It is the belief, in the Abrahamic faiths, that a seven-day cycle (and its completion in the eighth day) is fundamental to the law of God: the creation of the world in seven days, Noah sending out the dove after seven days, etc. Yet not only does God work in cycles of seven days, the seven-day cycle must also be observed in rituals that honor God: the observance of the sabbath, circumcision on the eighth day (“On the eighth day the flesh of his foreskin shall be circumcised” (Lev. 12:3). This became known not just as milah, “circumcision”, but something altogether more theological, brit milah, “the covenant of circumcision”. That is because even before Sinai, almost at the dawn of Jewish history, circumcision became the sign of God’s covenant with Abraham (Gen. 17:1-14), etc…
    In response to Maidhc: It sounds like you read my unabridged paper, linked above.
    For the benefit of those who haven’t, the Mesopotamians described the seven diatonic modes by naming seven intervals. Six of these intervals were always fifths; the seventh interval was always a diminished fifth (or tritone). They called the fifth interval “clear”, while they called the tritone interval “not clear”. To change the tuning of an instrument from one diatonic mode to another they simply “made clear” the tritone interval thereby automatically causing one of the original fifth intervals to become a tritone (or to be “not clear”). Repeating this process seven times generated the seven diatonic modes and the circle of fifths. This was an ingenious method, because all someone had to know to master the entire tuning system was how to tune an octave an a fifth (the tritone never needed to be tuned – only retuned as a fifth).
    Archaeological artifacts suggest that the first multiple-stringed instrument was invented (before 3000 BC) in the Near East and was later disseminated to Egypt and Greece. The angular harp, a slightly later invention (circa 2000 BC) also made its way to the western borders of modern-day China (the Tarim Basin). In my paper, cited above, there are photos of the angular harps discovered in Xinjiang, some that date to 1000 BC. There are also references to academic studies by Chinese scholars that link the Tarim Basin angular harps to the Near East.
    Also, in response to Maidhc: The Mesopotamian system is still very much in use today – the modern, Western system is virtually identical, except that, since approximately the last five centuries, the modern system has incorporated equal temperament.
    In response to Maxwell Martin: For a detailed description of the numbers in the table drawn on CBS 1766, please see Table 3, on page 21 of my unabridged paper, linked above.
    In response to AntC: Note that the Hebrew adoption of the seven-day week is always linked, by historians, to the Jewish Captivity in Babylon, in the sixth century BC. At this time, the Babylonians not only used a seven-day (non-continuious) week, they also used a musical system that was, at that time, already over 1000 years old – a system based on the sequence 4,1,5,2,6,3,7, and its inversions. Although there is no cuneiform proof that they connected this musical sequence to the seven-day week, Origen (via Celsus) tells us that this (the week-day) sequence is from “musical reasons, quoted by the Persian theology,” and we know that by the sixth century BC, the Persian Magi were active in Babylon.
    Also, in response to AntC: The Mesopotamians most certainly derived the circle of fifths. Here, for example, is an entry in Oxford Music Online ( The reference is in the second to last paragraph of the article: “It [Tablet UET VII 74] also demonstrates that the cycle of 5ths was known, and that the scales were named after the interval of a 5th or a 4th that initiated each of the seven tuning procedures…” To describe briefly: the circle of fifths was generated while constructing the seven diatonic modes. This process is identical to “Pythagorean Tuning”, which should actually be called “Mesopotamian Tuning.”
    It sounds as though you know a lot about ancient music theory, so I really hope you’ll read my paper. In it, you will learn that the sequence 4,1,5,2,6,3,7 is generated when creating a 12-tone scale from the circle of fifths using the ratios 2/3 and 2/1, a process known as the ancient Chinese sanfen sunyi method. A seven-pointed star resembling the one on CBS 1766 can then be derived from the mathematics that underlie this 12-tone scale.
    Also, in response to AntC: The sequence 4,1,5,2,6,3,7 is mathematically derived when creating a chromatic scale from the circle of fifths. The same sequence is also documented (1800 BC) as the basis of the Mesopotamian tonal system. (Incidentally, the number seven is known to have been used in musico-religious ceremonies of cosmological significance by the Mesopotamians as early as the third millennium BC.) The same sequence is also embedded in the ancient Chinese sanfen sunyi method, as early as the third century BC. It is also encoded in the Mithraic ladder ritual, as described by Origen (via Celsus). But the Mithraic ladder arrangement is very similar to one given by Herodotus, almost 800 years earlier, when he described the battlements of the ancient Persian city of Ecbatana:
    “The circles of the walls were, in all, seven. . . . The battlements of the first circle are white, the second black, the third scarlet, the fourth blue, the fifth orange. Thus the battlements of those five circles are painted with colors; but of the last two circles, the one had its battlements coated with silver, the other with gold.” Herodotus, The History of Herodotus, trans. D. Grene (University of Chicago Press, 1987), 80–81.
    The same sequence selects the notes in the major (diatonic) scale from the circle of fifths.
    In my opinion, the discovery of the sequence in the mathematics of music and the fact that seven planets were known set the ground work for reverence of the number seven (and the number twelve: the zodiac is first documented in Babylon circa 500 BC). Everything else followed…
    Again, to AntC: Yes, a musicologist did review my paper before it was published in SPP. Professor Lothar von Falkenhausen, eminent archeologist and musicologist at UCLA, had this to say regarding my paper:
    “Using sources previously unavailable, the article brings the two traditions closer together than ever before, and it certainly goes some way toward tipping the balance for the argument to diffusion over independent invention.” He goes on to explain: “The principal portion of the article, showing the mathematical-musicological parallels between tone-generation methods in ancient Mesopotamia and early China are extremely interesting and well presented. With respect to showing these parallels, and pointing out concrete structural similarities between China and Mesopotamia, it seems to me that the author is really making an important contribution.”
    In response to Kenny Easwaran: The ancient Chinese sanfen sunyi method (which was most likely adopted from the Near East in the first millennium BC: see my paper, linked above) was used in ancient China to generate the seven-note Lydian mode (in which the fundamental would have been described as “down-generated”). Source: Discourses of the States, “Discourses of Zhou”, C: “What are the seven [pitch] standards?” Note by Wei Zhao (204-273 AD): “The seven [pitch] standards are tuning devices. Huáng Zhōng is used for gōng. Tài Cù is used for shāng. Gū Xiǎn is used for jué. Lín Zhōng is used for zhǐ. Nán Lǚ is used for yǔ. Yìng Zhōng is used for biangong and Ruí Bīn is used for bianzhi.” As shown in my paper, the seven-pitches listed by Wei Zhao generate the Lydian mode (the ancient Chinese had twelve names for the twelve pitches in the circle of fifths, and those listed by Wei Zhao are seven of them).
    It is also probable that ancient Chinese used the Ionian mode, as evidenced by a set of 14 bells (the "Biao Bells"), which date to the 6th century BC and which play a few octaves of the Ionian mode. (Source: Robert Bagley, “The Prehistory of Chinese Music Theory,” Proceedings of the British Academy 131 (2005): p78). The ancient Chinese sanfen sunyi method would describe the Ionian mode as having an “up-generated” fundamental.
    Also of note:
    “Only after the numbers are made to accord and the musical notes are harmonized will things be unified. Therefore, the number seven is used to unify their number, and the standard pitches are used to harmonize the notes. And thus it is that there are seven pitches.” Guo Yu (fifth century BC).
    In response to Gregory Kusnick: The first source that mentions the planetary hour reason for the week-day order is Cassius Dio (155-235 AD). But this explanation was one of two given by Dio (in fact, it was the second one). Dio’s first explanation is musical:
    …if you apply the so-called “principle of the tetrachord” (which is believed to constitute the basis of music) to these stars, by which the whole universe of heaven is divided into regular intervals, in the order in which each of them revolves, and beginning at the outer orbit assigned to Saturn, then omitting the next two named the lord of the fourth, and after this passing over two others reach the seventh, and you then go back and repeat the process with the orbits and their presiding divinities in this same manner, assigning them to the several days, you will find all the days to be in a kind of musical connection with the arrangement of the heavens. (Cassius Dio, Roman History, Book XXXVII, Chapter 18).
    How did this first, musical reason get forgotten? Because scholars who didn’t understand it, simply dismissed it. For example, H. Chadwick, in his translation of Origen’s Contra Celsum, wrote the following:
    “The order of the planets in [the] Mithraic list is not the usual order based on the ancient view of their distances from earth (Saturn, Jupiter, Mars, Sun, Venus, Mercury, Moon), but that of the days of the week. Evidently, Celsus mentioned explanations of this order derived from Pythagorean musical theory. Dio Cassius (XXXVII 18–19) also gives two explanations of the planetary week. The second is now regarded as correct. The first is based on the principle of the tetrachord, and is no doubt one of the two mentioned by Celsus.” (Origen, Contra Celsum, trans. H. Chadwick (Cambridge University Press, 1965), 335, footnote 2).
    My hunch is that, over time, the musical reason was dismissed so often that it has simply been forgotten. Perhaps someone would re-include it in the Wikipedia “week’ page, and give a link to this LL post? Please do, it would be very much appreciated…

  28. Sara de Rose said,

    May 8, 2022 @ 10:03 am

    I’ve created this short Youtube video, which basically duplicates the information contained in the original post. I ask that anyone interested in furthering this discussion watch the video and share it. Thank you. Video link: “The Musical Origin of the Seven-day Week” :

  29. Annie Gottlieb said,

    May 8, 2022 @ 11:58 am

    So the "Pythagorean comma" is sort of like the leap second?

    Again this intimacy between music and time. "Time signatures," "keeping time" . . .

  30. AntC said,

    May 8, 2022 @ 6:43 pm

    Thank you Sara, and welcome! There's a lot to digest, I'll take some time.

    So the "Pythagorean comma" is sort of like the leap second?

    Well for some value of 'like'/'similar'. What we have in both astronomy and harmonics is a load of approximations/coincidences. And kludges to line things up.

    There's no reason to expect the period of spin of the earth would have any relation to the period of moon cycles or to the period of earth revolving around the sun. Nor to the periods of planetary motion as viewed from the earth.

    The period of the spin of the earth is much shorter than a moon cycle, so let's round that to 28 days; and very much shorter than revolving around the sun, so let's call that 365 days. 28 almost exactly divides into 365; 7 does divide exactly into 28. Those are all coincidences. (The Greeks rounded to 360 for degrees of a circle, so they had plenty of factors to divide into.)

    How shall we punctuate our daily lives? A stretch over 28 days is too long to pay attention to in a mostly non-literate society. The Romans divided months at the Ides and the Nones — but this gives somewhat irregular punctuation. A persistent cycle of 7 days is a good fit mathematically.

    I don't think we need any more explanation than that as to where 7 came from. Having chosen 7, we then see mystical coincidences. (In the same vein, the alleged spacing of the five planets for their orbits to fit inside a nesting of the Platonic solids is also just a mystical coincidence. Another coincidence with human female cycles gets them called 'menstrual' — that is, moon-based. Other mammals have 'menstrual' cycles varying between 9 and 37 days, depending on the species. Biorhythms include a 28-day cycle. It seems humans just can't help themselves wanting to explain numerical coincidences. See Kabbalah.)

  31. AntC said,

    May 8, 2022 @ 7:07 pm

    One harmonic approximation that is significant for Western music, derived not from 'fifths' but the next overtone, is 'thirds' at a ratio 5:4. A harmonic third played with the 'fifth' gives the major triad.

    Three intervals of a major third gives an octave — but this is another coincidence/a terrible approximation. The harmonically-derived third is also not a good fit to the third obtained via the circle of fifths.

    At what stage did harmony and polyphony enter Western music, needing different notes to 'sound together'? Other musics I'm aware of have a single melodic line played over drums or drones accompaniment.

    It's been observed (from memory this is traditions in Eastern Europe) that unaccompanied choristers will sing at the fifth and even at the (natural harmonic) third.

  32. Andrew Usher said,

    May 8, 2022 @ 8:19 pm

    The 'planetary hours' explanation is mathematically the same as the 'tetrachord' one, as both generate an arithmetic progression mod 7, increment 4, i.e. 4,1,5,2,6,3,7 when zero is not accepted. This is not, as stated by Gregory Kusnick, a coincidence. I don't know why the hours theory is the accepted one, but I assume there are reasons and I don't see anything here that would rebut any.

    k_over_hbarc at

  33. AntC said,

    May 8, 2022 @ 11:10 pm

    I'm sorry Sara, there's nothing new in your video as compared to the paper. And I find nothing convincing connecting the seven-day week to the methodology of the CBS 1766 tablet.

    If that tablet hadn't mistakenly been taken in 1929 to be for day-naming/astronomical purposes, would we even be having this conversation?

    The critical question is: did the Mesopotamians/Persians/Babylonians operate a seven-day week? If so, how did they name the days?

    "A continuous seven-day cycle that runs throughout history … was first practiced in Judaism, dated to the 6th century BC at the latest … " I already quoted from wikipedia. (The wiki hypothesises/your video repeats the Judaic system was acquired during captivity with the Babylonians — but they had a variable-length fourth 'week' of the month to keep aligned with phases of the moon. Hence not a fixed cycle of seven. Hence naming for exactly seven heavenly bodies doesn't work.) The Judaic day-names don't relate to astronomy.

    For me this is conclusive evidence the 7 comes from dividing a 28-day moon cycle. Nothing to do with tuning cycles.

    Your video jumps from The Mesopotamian/Persian musical system ~2,500 BC; to the tablet ~1,800 BC; to Judaism adopting the 7-day week C6th BC to Origen of Alexandria/Mithraists third Century AD — after adopting Judaic/Christianity's seven-day week.

    You do not show causation/cultural transmission. Only just-so stories.

    That's a huge span of time for the significant number 7 to acquire all sorts of mystical associations/noted coincidences which were simply no consideration in 6th century BC.

    The association of the days of the week with the Sun, the Moon and the five planets visible to the naked eye dates to the Roman era (2nd century). [wiki]

    To repeat myself: if not for the coincidence the Romans could see only seven heavenly bodies (excepting the 'fixed stars'), would we be even having this conversation?

    It's a mathematical coincidence that if you repeatedly exponentiate tripling (being the first 'interesting' ratio after doubling), you'll eventually come to a number close to a power of two, so repeatedly halving will get back close to where you started. The number of exponentiations happens to be 7 triplings. Making the exponentiating ratio 3:2 (a 'fifth') and halving (moving down an 'octave') in alternating exponents is just mystification.

    @Andrew as both generate an arithmetic progression mod 7, increment 4

    But why pick 7? Because of the coincidence between the already-established 7 days of the week and the happenstance of 7 visible bodies. And why pick 4?

    If there weren't 7 heavenly bodies, I daresay Mithraists could have dreamt up some explanation involving the 7 hills of Rome. And they'd have found a 4 from somewhere.

    I'm all done with names of the days. There's a much more interesting question of whether the Mesopotamian tuning system was adopted by the Greeks/Romans and/or by the Chinese.

  34. AntC said,

    May 9, 2022 @ 12:02 am

    Lothar von Falkenhausen is Professor of Chinese Archaeology and Art History at UCLA …
    He has published copiously on musical instruments, …

    He has an impressive resumé. I see Archaeology and instruments as cultural artefacts/in ritual; I don't see music theory.

    The specific musicological question I want to examine is: given that these tunings arise from physics/natural harmonics; could they have been invented only once in one place, then transmitted culturally; or could they have been independently discovered multiple times?

    How could we investigate that? Especially amongst cultures remote from Mesopotamia and/or without writing — because musical practices could be transmitted alongside writing.

    Most musical instruments are made of perishable materials, so would disappear from the archaeological record — or at least enough detail to know their tuning would. For example, Meso- and South American indigenous cultures had tuned musical instruments (like pan pipes, ocarinas) prior the European invasions. Do we know how they were tuned?

  35. maidhc said,

    May 9, 2022 @ 5:25 am


    If you want to derive a major triad either from the circle of 5ths or from the harmonic series, you don't have to go too far to get the major third.

    The big problem in the major/minor system is that you have to go a long way to get that minor third. There's not much justification for why it should be considered the equivalent of the major.

    The modal system produces various minor modes, but they are not the same as the modern (western European) classical system. Not that there's anything wrong with that system, but you can't really claim it's based on physics. Just appreciate it for what it is.

    Sara de Rose:
    Harmonic systems based on the "Greek" modal model are still found in Western Europe, but in the regions closest to the Babylonian heartland, in klezmer, Balkan, Arabic, Persian and Indian music, things have taken a much different direction since the Muslim expansion of the 7th century or so. Why did the old system collapse?

  36. Gregory Kusnick said,

    May 9, 2022 @ 10:05 am


    It's true that both rules generate the same sequence by counting 4 against 7 — or, equivalently, decrementing by 3. But as Ant asks, where does the 4 or 3 come from?

    In the planetary hours rule, the 3 comes from 24 modulo 7. In the tetrachord rule, it comes from treating planetary orbits as keys on a piano keyboard and counting off by fourths. Since the definition of a musical fourth has nothing to do with the number of hours in a day, that makes it a coincidence in my book.


    How did this first, musical reason get forgotten? Because scholars who didn’t understand it, simply dismissed it.

    Or maybe they did understand it, and dismissed it on grounds of parsimony. If the sequence of weekday names can be adequately explained in terms of astronomical quantities (number of planets, length of a day), then what additional explanatory power is gained by bringing musical theory into it? None, as far as I can see.

  37. Sara de Rose said,

    May 9, 2022 @ 10:07 am

    The sequence 4,1,5,2,6,3,7 is generated by “gearing” cycles of 7 and 12 (and also cycles of 7 and 5 because, as Andrew Usher pointed out, 12 and 5 are the same in mod 7). To someone not familiar with this mathematical jargon, there’s an easy way to illustrate this.
    First, to illustrate the gearing of 7 and 5, write the numbers 1 through 7 five times, as shown below. Now, circle the first number and every subsequent fifth number (count by including, each time, the last circled number):
    You come out with the sequence 1,5,2,6,3,7 (an inversion of the sequence 4,1,5,2,6,3,7). If we were to continue on writing numbers and circling them, the sequence would be generated indefinitely.
    Now, here’s how to illustrate the gearing of 7 and 12. Do the same thing as above, but write the numbers 1 through 7 twelve times instead of five. Now, circle the first number and every subsequent twelfth number (count by including, each time, the last circled number):
    Once again, you come out with the sequence 1,5,2,6,3,7,4.
    So, this is where the sequence 4,1,5,2,6,3,7 comes from, but how does it relate to music? And why do I start it with the number 4?
    An octave is a natural harmonic phenomenon: when a high voice and a low voice sing the same melody together, the two voices naturally sing an octave apart. When doing this, the two voices blend seamlessly – but they are not singing the same notes, instead every note sung by the higher voice is the higher octave of the lower voice.
    To play an octave on a musical string, one simply plays the whole string (the lower voice, described above) and then shortens the string exactly in half. Then, playing the half string one hears the higher octave (the higher voice, described above). From this, a mathematical relationship emerges: octave = 1/2.
    Now let’s divide the string into the next possible smallest number of parts: three parts. If we play 1/3 of the string, we hear a new note. If we play 2/3 of the string, we hear this new note again, but this time an octave lower. (Why? Because 1/3 is one half of 2/3, so the two notes are an octave apart.) Today, we call the note sounded by 2/3 of the string, the ‘fifth’, because if the whole string plays the first note of a major scale (C, for example), playing 2/3 of the string will sound the fifth note of the same scale (G, to continue the example). Here, we have another mathematical relationship: fifth = 2/3.
    The ancient Chinese sanfen sunyi method (very probably transmitted from Mesopotamia with the angular harp, circa 1000 BC) make use of just these two ratios, 1/2 and 2/3, to generate a chromatic scale, and it is in this gearing of the cycles of the octave and the fifth that the numbers 7 and 12 appear. Here’s how:
    If one generates consecutive fifths [the first fifth having 2/3 of the length of the whole string; the second fifth having 2/3 x 2/3 (or 4/9) of the length of the whole string; the third fifth having 2/3 x 2/3 x 2/3 (or 8/27) of the length of the whole string, and so on…] the twelfth fifth will have a string length of (2/3)12 or 4096/531441 = .0077073.
    The string length of the twelfth fifth (.0077073) is important to note, because it is very close to the string length of the seventh higher octave of the whole string: (1/2)7 or 1/128 = .0078125. In other words, twelve fifths span seven octaves, with a very small discrepancy (.0078125/.0077073 = 1.0136433), a difference known as the ‘Pythagorean comma’.
    Twelve fifths span seven octaves, but it’s only on a relatively modern instrument – the piano (and its earlier relatives) – that we can hear seven octaves and therefore hear all twelve fifths. For our distant ancestors to hear all twelve fifths on a musical string, a fundamental realization had to be made (and this realization is incorporated into the ancient Chinese sanfen sunyi method, circa third century BC): that every fifth can be moved into the very lowest octave by doubling its string length, anywhere between one and seven times, depending on its original position relative to the first octave.
    Moving the twelve fifths down through seven octaves, so that all twelve fifths are in the lowest octave (creating, by the way, the familiar pattern of frets on stringed instruments) is, in fact, an example of the gearing of cycles of 7 and 12. Consequently, when creating a 12-tone scale from twelve consecutive fifths (which is what the sanfen sunyi method does) the sequence 4,1,5,2,6,3,7 is generated – and it begins with the number 4. To learn more, watch the video: “The Origin of the Sequence 4,1,5,2,6,3,7” ( or read from page 17 to page 46 in my SPP paper (linked above).
    To recap, the sequence 4,1,5,2,6,3,7 is generated when gearing the cycles of the octave and the fifth. This is a mathematical truth, not an arbitrary human convention. As Andrew Usher pointed out, the mathematics behind the ‘planetary hours’ explanation of the week-day order is the same, but there is, nevertheless, one very important difference:
    The octave and the fifth are innate mathematical/musical cycles while the division of the day into 24 (or two times 12) hours is completely arbitrary. The listing of seven planets is, of course, also arbitrary. These two cycles combine to create Dio’s ‘planetary hours’ explanation, but both are arbitrary human constructs – not mathematical truths.
    Combine this with the fact that Dio actually gives two reasons for the week-day order, and that the first reason he cites is musical, and we have strong support for the theory that the week-day order is drawn, as Origen put it “from musical reasons…quoted by the Persian theology”.
    In response to AntC: The Mandeans, native to Iraq, name the days of the week using their ancient Babylonian names. (see page 129-130 of my paper). Also, thanks for quoting Falkenhausen, who is, by the way, very supportive of my thesis (see quote from him in my previous comment).
    In response to maidhc: Tablet CBS 10996 (Babylon 700 BC) lists fourteen intervals. Seven of these (six fifths and one tritone) are referred to in the tuning instructions on tablet UET VII 74 (1800 BC) – instructions which derive the seven diatonic modes. The remaining seven intervals are all major or minor thirds (see Table 14 on pg 75 of my paper). PS. I have no idea why the old system collapsed in the Babylonian heartland.
    My final comment:
    The generation of the sequence 4,1,5,2,6,3,7 is a mathematical truth. A seven-pointed star resembling the one on tablet CBS 1766 can be derived from this mathematics. In other words, the sequence and diagram are derived from a rational exploration of the simple mathematics of music – an exploration which almost certainly was one of the first forays into abstract mathematics.
    I believe that the discovery of this sequence and the related seven-pointed star in the mathematics of music inspired our ancestors to consider (con =with; sider=star) that music somehow played a role in cosmic order. Because, for them, there were seven planets. (By the way, I’m curious as to when a star shape became associated with a star in the sky. Could this date back to a belief that there is a connection between music and cosmology?)
    I also wonder if the zodiac, which is an arbitrary division of the ecliptic into 12 constellations, which dates back to 5th century BC Babylon, could have been inspired by the much earlier (tablet UET VII 74, 1800 BC) knowledge of the circle of fifths. In other words, did the Babylonians attempt to map out the cosmos using a musical template? If this is the case, other factors may have contributed: for example, the fact that the ratio between the duration of the solar year and the duration of the “lunar year” (twelve full cycles of the phases of the moon) is 365.25/354.37 = 1.0307…a value reminiscent of the “Pythagorean comma”.
    I will now let this topic lie, and have my paper speak for itself. I will soon post, however, at Victor Mair’s suggestion, a short description of the angular harps discovered in the Tarim Basin.
    Thanks for the stimulating discussion,

  38. M. said,

    May 9, 2022 @ 3:57 pm

    @ Sara. Thank you for your detailed clarifications.

    Please consider this friendly suggestion: in future, skip a line between paragraphs.

  39. AntC said,

    May 9, 2022 @ 5:48 pm

    The ancient Chinese sanfen sunyi method (very probably transmitted from Mesopotamia with the angular harp, circa 1000 BC)

    Please point to the evidence for this transmission. AFAICT from your paper, the angular harp got only as far as the Tarim basin/ illustration in the DunHuang Caves. That was not China at the time. (Many of us think it should not be China today.)

    There is no archaeological proof that the specific type of angular harp excavated in Xinjiang made its way deeper into China. Nevertheless, music archaeologist B. Lawergren suggests that the Xinjiang harps had an influence on the design of later Chinese stringed instruments. [p 9]

    It's a long way from "influence" to 'adopted the same tuning system' — especially since the Chinese qin appears to have 10 strings vs the angular harp's 7 (heptatonic). (I don't see the shape of the qin being very similar — even as vaguely as Lawergren's "inspired the shape".) He does concede

    [The from-Mesopotamian harp] ended up with five strings, and this probably implies it had severed any association with the Mesopotamian tuning theory. It arrived in Xinjiang without the theoretical framework.

    There follows some discussion of earlier 5-string harps in China. That would be consistent with a pentatonic scale, that would need only a few steps of fifths up/down. Not enough to realise it forms a cycle.

    There's also mention of 9-string lyres, based possibly on Mesopotamian models. Richard Dumbrill, who has also analysed CBS 1766, is of the view the 9-string lyres used a different tuning system, not heptatonic.

    The trouble is we can't know how those other instruments were tuned. Did the 9 or 10 strings span more than an octave? (Dumbrill thinks so — with an alarming level of interpolation into the fragments of writings.) The 25-string Chinese se presumably had/has more than 7 tones within an octave.

    If all that remained of the 'theoretical framework' after dispersion through the Silk Road was 'use the second harmonic' (fifths), that's really no different to 'use your ears' and listen for the resonance. Figuring out the cycle/Pythagorean comma could have been independently rediscovered.

    But then many in the field (including Lawergren) want so hard for Mesopotamia to be the one source of all music, they're pushing claims beyond what the evidence will support.

    Adding all this Numerology/Astrology about days of the week is subtracting from credibility.

  40. AntC said,

    May 9, 2022 @ 6:39 pm

    'use your ears'

    beyond what the evidence will support

    I see a couple of parallels:

    In Historical Linguistics, there are 'lumpers' who think they can 'extend' the Comparative Method to reconstruct Proto-languages. There's a even a team claiming to reconstruct some vocabulary of what they call Proto-Sapiens. The trouble is, no-one can point to counter-evidence. We just can't tell — is the point.

    In music, there's been some celebrated copyright cases where artists have been accused of 'stealing' ideas: George Harrison, Robin Thicke/Pharrell Williams, Mariah Carey, Katy Perry, …. Putting these cases in front of a jury (people who only listen to music, and that probably only a few genres) produces outlandish damages awards. Yes those songs do sound similar; that's because they sound similar to a whole tradition of styles, memes, chord changes. Professional musicians are outraged at these awards: You can't own the Minor scale (at less than a minute in, Adam's found a parallel from Katy Perry to a rapper to a Bach Violin Sonata. Wait for the take-down starting 6:15.)

    Similarly, you can't own tuning-by-fifths. It's inevitable you'll exhaust the 'interest' in octaves pretty quickly; 'use your ears' you'll find fifths by overblowing a horn or stopping a string; muck about with this for a while, you'll find other resonances. Yes you need some sophisticated maths to regularise the tuning when you get to tones that don't resonate. That doesn't mean you must have taken the maths from another culture.

  41. AntC said,

    May 9, 2022 @ 9:09 pm

    (By the way, I’m curious as to when a star shape became associated with a star in the sky. Could this date back to a belief that there is a connection between music and cosmology?)

    The Egyptian hieroglyph representing "star" had five points, while the "star" sign in Mesopotamian cuneiform had eight.
    Sopdet, the Egyptian personification of the star Sirius, is always shown with the five-pointed star hieroglyph on her head.

    The Sumerian sign DIĜIR [see symbol at link] originated as a star-shaped ideogram indicating a god in general, or the Sumerian god An, the supreme father of the gods. Dingir also meant sky or heaven …

    By the time of Late Babylonian/Assyrian the cuneiform got simplified to a cross-like symbol with an extra wedge — i.e. four or maybe five points, not seven.

    Star of David has six points "A derivation of the Seal of Solomon, which was used for decorative and mystical purposes by Muslims and Kabbalistic Jews, …"

    Starfishes have five points usually.

    "In alchemy, a seven-sided star can refer to the seven planets which were known to early alchemists, and also, the seven alchemical substances: fire, water, air, earth, sulphur, salt and mercury." (There's some more coincidences with 7.)

  42. Victor Mair said,

    May 16, 2022 @ 6:38 pm

    From Larry T.:

    Regarding week days and music.

    Gregory wrote: “we accept the law concerning the octave which cleanses and circumcises because once time represented by the number seven comes to a close, the octave succeeds it.

    Indeed. In Judaism the circumcision is done on the 8th day after the birth.

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