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Thread: Why Is C Major Called A "Diatonic" Scale"? What Does "Diatonic" Mean?

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    12 is a composite number = 2^2 x 3, so only 1/11 or 5/7 can serve as generators for the cyclic group of 12 pitches.
    Compare to 34 equal (which is better than any meantone tuning in terms of harmonic accuracy) where the circle of fifths gives us...17 equal, so obviously tonal modulation and chord patterns there are different than these in 12 equal music theory.

    (12 equal has subgrous C2, C3, C4 and C6. A coset of Cn is obtained by adding to each element of Cn the same element of Cn. Example: tempered fully diminished chord is C4 in 12 equal and is represented in atonal integer notation as (0,3,6,9). The other cosets are 1,4,7,10 and 2,5,8, 11. Obviously in 34 equal we have 17 equal and tritones (of course, any tuning, divisible by 2 has this one) as subgroups. We can construct all the modes of limited transposition, various looping chord progressions and represent various other elements as generated by these cosets or intervals in them. For reference, check any abstract algebra/group theory text/wikipedia.)

    From
    https://en.wikipedia.org/wiki/Modulatory_space

    "Toroidal modulatory spaces

    If we divide the octave into n parts, where n = rs is the product of two relatively prime integers r and s, we may represent every element of the tone space as the product of a certain number of "r" generators times a certain number of "s" generators; in other words, as the direct sum of two cyclic groups of orders r and s. We may now define a graph with n vertices on which the group acts, by adding an edge between two pitch classes whenever they differ by either an "r" generator or an "s" generator (the so-called Cayley graph of Z 12 with generators r and s). The result is a graph of genus one, which is to say, a graph with a donut or torus shape. Such a graph is called a toroidal graph.

    An example is equal temperament; twelve is the product of 3 and 4, and we may represent any pitch class as a combination of thirds of an octave, or major thirds, and fourths of an octave, or minor thirds, and then draw a toroidal graph by drawing an edge whenever two pitch classes differ by a major or minor third.

    We may generalize immediately to any number of relatively prime factors, producing graphs can be drawn in a regular manner on an n-torus. "


    Translated in more normal language we can say that every interval in 12 equal can be decomposed into major thirds and minor thirds -example: P5=M3 + m3

    So we don't need chains or circles of generators to get to diatonic or 12 tone (tuned to equal, meantone, just intonation, diaschismic like 34, schismic or whatever temperament). Of course, there exist even more different methods to construct 7note diatonic/12 equal.

    If we are that concerned about very good perfect fifths, the only alternative to diatonic scale actually is 17 notes and this is based on some patterns of log3 base2 - we get 8 major chords, 8 minor chords and one dissonant chord. Pythagorean/syntonic commas becomes a small step in this tuning. I guess this is similar to some kind of Indian music gamut. 41 equal or 53 equal supports it.
    Last edited by BabyGiraffe; Jul-30-2019 at 09:55.

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    Senior Member millionrainbows's Avatar
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    Thank you, BabyGiraffe, that clears everything up!
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    Quote Originally Posted by Woodduck View Post
    A clear case of diamentia.
    "The way out is down the toilet; why is it that more people do not use this method?'
    "The way out is through the door. Why is it that no one will use this method?"
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    The tetrachords which make up the C major diatonic scale, when used as a scale, both have leading tones. The first implies F, the second implies C. Thus, the C major scale has "two tonics" and is "ditonic" in keeping with the original Greek root, which can mean two things. I'm on solid ground.
    "The way out is through the door. Why is it that no one will use this method?"
    -Confucious

    "In Spring! In the creation of art it must be as it is in Spring!" -Arnold Schoenberg

    "We only become what we are by the radical and deep-seated refusal of that which others have made us." -Jean-Paul Sartre

    "I don't mind dying, as long as I can still breathe." ---Me

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    Quote Originally Posted by millionrainbows View Post
    The tetrachords which make up the C major diatonic scale, when used as a scale, both have leading tones. The first implies F, the second implies C. Thus, the C major scale has "two tonics" and is "ditonic" in keeping with the original Greek root, which can mean two things. I'm on solid ground.
    We've all made factual mistakes and admitted them on here. There's really no shame in it!

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    Quote Originally Posted by isorhythm View Post
    We've all made factual mistakes and admitted them on here. There's really no shame in it!
    That's OK if you are ignorant!
    "The way out is through the door. Why is it that no one will use this method?"
    -Confucious

    "In Spring! In the creation of art it must be as it is in Spring!" -Arnold Schoenberg

    "We only become what we are by the radical and deep-seated refusal of that which others have made us." -Jean-Paul Sartre

    "I don't mind dying, as long as I can still breathe." ---Me

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    The prefix dia in Greek means across or through. Diameter (across or through a circle), diatonic (through the tones).

    https://pressbooks.bccampus.ca/greek...reek-prefixes/

    Not 2 of anything. To force the relation of diatonic to 2 tonics is like forcing a relationship between Hitler and Christianity
    "Forgive me, Majesty. I'm a vulgar man. But I assure you, my music is not.“ Mozart

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    Quote Originally Posted by Phil loves classical View Post
    The prefix dia in Greek means across or through. Diameter (across or through a circle), diatonic (through the tones).
    Yeah, yeah, we know all that. I also pointed out that the Greek root has 2 meanings.
    "The way out is through the door. Why is it that no one will use this method?"
    -Confucious

    "In Spring! In the creation of art it must be as it is in Spring!" -Arnold Schoenberg

    "We only become what we are by the radical and deep-seated refusal of that which others have made us." -Jean-Paul Sartre

    "I don't mind dying, as long as I can still breathe." ---Me

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    Quote Originally Posted by millionrainbows View Post
    Yeah, yeah, we know all that. I also pointed out that the Greek root has 2 meanings.
    Yes, that was quite the virtuosic display of confirmation bias

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    Quote Originally Posted by millionrainbows View Post
    The tetrachords which make up the C major diatonic scale, when used as a scale, both have leading tones. The first implies F, the second implies C. Thus, the C major scale has "two tonics" and is "ditonic" in keeping with the original Greek root, which can mean two things. I'm on solid ground.
    Once again, this is false. This "original Greek root" to the term diatonic is your fabrication. There is no ground supporting your position. You continue to fill this thread with misinformation. Just admit you were wrong already.

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    Quote Originally Posted by millionrainbows View Post
    • Thank you, BabyGiraffe, I'll take that into consideration.
    • The English word diatonic is ultimately from the Greek διατονικός (diatonikós), itself from διάτονος (diátonos), which may mean (as OEDclaims) "through the tones" (taking τόνος, tónos, to mean interval of a tone), or perhaps stretched out (as recorded in Liddell and Scott's Greek Lexicon). See also Barsky (Chromaticism, Barsky, Vladimir, Routledge, 1996, p. 2): "There are two possible ways of translating the Greek term 'diatonic': (1) 'running through tones', i.e. through the whole tones; or (2) a 'tensed' tetrachord filled up with the widest intervals". The second interpretation would be justified by consideration of the pitches in the diatonic tetrachord, which are more equally distributed ("stretched out") than in the chromatic and enharmonic tetrachords, and are also the result of tighter stretching of the two variable strings. It is perhaps also sounder on linguistic morphological grounds. (See also Merriam-Webster Online.)
    • A completely separate explanation of the origins of the term diatonic appeals to the generation of the diatonic scale from "two tones": "Because the musical scale is based entirely on octaves and fifths, that is, two notes, it is called the 'diatonic scale' " (Phillips, Stephen, "Pythagorean aspects of music", in Music and Psyche, Vol. 3, available also online. But this ignores the fact that it is the element di- that means "two", not the element dia-, which has "through" among its meanings (see Liddell and Scott). There is a Greek term δίτονος (dítonos), which is applied to an interval equivalent to two tones. It yields the English words ditone and ditonic (see Pythagorean comma), but it is quite distinct from διάτονος.
    • Yet another derivation assumes the sense "through the tones" for διάτονος, but interprets tone as meaning individual note of the scale: "The word diatonic means 'through the tones' (i.e., through the tones of the key)" (Gehrkens, 1914, see below; see also the Prout citation, at the same location). This is not in accord with any accepted Greek meaning, and in Greek theory it would fail to exclude the other tetrachords.
    • The fact that τόνος itself has at least four distinct meanings in Greek theory of music contributes to the uncertainty of the exact meaning and derivation of διατονικός, even among ancient writers. (See Solon Michaelides, The Music of Ancient Greece: An Encyclopaedia (London; Faber and Faber, 1978), pp. 335–40: "Tonos".
    • Τόνος may refer to a pitch, an interval, a "key" or register of the voice, or a mode.) For more information, especially concerning the various exact tunings of the diatonic tetrachord, see Diatonic genus.


    Hmm, two tones, two tetrachords, two semitones, two keys...
    I was impressed with your research and knowledge here, until I discovered you simply copied and pasted a Wikipedia footnote.

    https://en.wikipedia.org/wiki/Diatonic_and_chromatic (footnote 8)

    You did add lots of boldface, large fonts and red coloring, though.

    Reading it in Wikipedia, I was drawn to this sentence:

    But this ignores the fact that it is the element di- that means "two", not the element dia-, which has "through" among its meanings (see Liddell and Scott). There is a Greek term δίτονος (dítonos), which is applied to an interval equivalent to two tones. It yields the English words ditone and ditonic (see Pythagorean comma), but it is quite distinct from διάτονος.
    Last edited by jegreenwood; Aug-03-2019 at 14:53.

  15. #42
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    Quote Originally Posted by EdwardBast View Post
    Once again, this is false. This "original Greek root" to the term diatonic is your fabrication. There is no ground supporting your position. You continue to fill this thread with misinformation. Just admit you were wrong already.
    The English word diatonic is ultimately from the Greek διατονικός (diatonikós), itself from διάτονος (diátonos), which may mean (as OEDclaims) "through the tones" (taking τόνος, tónos, to mean interval of a tone), or perhaps stretched out (as recorded in Liddell and Scott's Greek Lexicon). See also Barsky (Chromaticism, Barsky, Vladimir, Routledge, 1996, p. 2): "There are two possible ways of translating the Greek term 'diatonic': (1) 'running through tones', i.e. through the whole tones; or (2) a 'tensed' tetrachord filled up with the widest intervals". The second interpretation would be justified by consideration of the pitches in the diatonic tetrachord, which are more equally distributed ("stretched out") than in the chromatic and enharmonic tetrachords, and are also the result of tighter stretching of the two variable strings. It is perhaps also sounder on linguistic morphological grounds. (See also Merriam-Webster Online.)
    A completely separate explanation of the origins of the term diatonic appeals to the generation of the diatonic scale from "two tones": "Because the musical scale is based entirely on octaves and fifths, that is, two notes, it is called the 'diatonic scale' " (Phillips, Stephen, "Pythagorean aspects of music", in Music and Psyche, Vol. 3, available also online. But this ignores the fact that it is the element di- that means "two", not the element dia-, which has "through" among its meanings (see Liddell and Scott). There is a Greek term δίτονος (dítonos), which is applied to an interval equivalent to two tones. It yields the English words ditone and ditonic (see Pythagorean comma), but it is quite distinct from διάτονος.
    Yet another derivation assumes the sense "through the tones" for διάτονος, but interprets tone as meaning individual note of the scale: "The word diatonic means 'through the tones' (i.e., through the tones of the key)" (Gehrkens, 1914, see below; see also the Prout citation, at the same location). This is not in accord with any accepted Greek meaning, and in Greek theory it would fail to exclude the other tetrachords.
    The fact that τόνος itself has at least four distinct meanings in Greek theory of music contributes to the uncertainty of the exact meaning and derivation of διατονικός, even among ancient writers. (See Solon Michaelides, The Music of Ancient Greece: An Encyclopaedia (London; Faber and Faber, 1978), pp. 335–40: "Tonos".
    Τόνος may refer to a pitch, an interval, a "key" or register of the voice, or a mode.) For more information, especially concerning the various exact tunings of the diatonic tetrachord, see Diatonic genus.
    "The way out is through the door. Why is it that no one will use this method?"
    -Confucious

    "In Spring! In the creation of art it must be as it is in Spring!" -Arnold Schoenberg

    "We only become what we are by the radical and deep-seated refusal of that which others have made us." -Jean-Paul Sartre

    "I don't mind dying, as long as I can still breathe." ---Me

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    I have no idea how you can't read that and not immediately recognize how wrong you are. The note quite clearly says that whatever ignorant writer proposed that "diatonic" means "two tones" ignores the basic and indisputable fact that dia- comes from the Greek preposition meaning "through" or "across."

    An ancient Greek writer would not have confused the two. The precise meaning διατονικός is up for debate, but at no point is the number "two" a part of that.

    How many Classics PhDs will it take for you to just admit you, having no Greek, are just wrong here?

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    No PhD in classics, but as a reader of Ancient Greek and Latin, I fully support AeolianStrains, and Millionrainbows, you’re rather off the mark.

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    Quote Originally Posted by ECraigR View Post
    No PhD in classics, but as a reader of Ancient Greek and Latin, I fully support AeolianStrains, and Millionrainbows, you’re rather off the mark.
    Well, that's charming! I'll buy you a cake so you can have a little party!

    Meanwhile, jegreenwood and I will have a drink out in the garden.
    Last edited by millionrainbows; Aug-04-2019 at 13:25.
    "The way out is through the door. Why is it that no one will use this method?"
    -Confucious

    "In Spring! In the creation of art it must be as it is in Spring!" -Arnold Schoenberg

    "We only become what we are by the radical and deep-seated refusal of that which others have made us." -Jean-Paul Sartre

    "I don't mind dying, as long as I can still breathe." ---Me

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