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I know the dominant seventh chords include a 7th harmonic and there are progressions using them. What about utilizing higher harmonics? Maybe an add6 chord implies the ratio 13/8 for some certain places?

For instance in i - bIII - IV7 - iv(add6) progression, I suspect the added 6th can serve as the 13th harmonic of the fourth. I lowered the major second of scale to 13/12(at about 138 cents) and it sounds natural to my ears(maybe cause i used to the middle eastern music :) . Also, it seems lowering the minor third degree about 10 cents results a better dominant seventh experience.

Not directly related with the specific progression above but since the topic is in general about the usage of higher harmonics, here is an arrangement of a piece originally written for oud, arranged by professional Turkish classical guitarist Celil Refik Kaya. He says in the description that he transposed the piece to tonic B and the C is bent up about 40 cents. I think that bend is to nail the 13/12 ratio.

I strongly recommend anyone to watch the performance and listen to this beautiful piece.

  • Does iv(add6) mean you're adding a major or minor sixth? Also, what minor third degree are you talking about? The interval from the fifth to the seventh of a dominant seventh chord? Ten cents isn't nearly enough for that. The harmonic seventh is 31 cents low compared to an equal-tempered minor seventh, but a just-tempered fifth-plus-minor-third is 18 cents high compared to equal, or 49 cents higher than the harmonic seventh. – phoog Jun 19 '19 at 18:30
  • adding major sixth makes more sense than minor but i am talking about adding 13/8 sixth which is in between. I know the 7/6 is located much lower but I don't want to ruin the 6/5 minor third so somewhere in between works fine. – Ahmet Bilal Jun 19 '19 at 20:30
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Once you get above the sixth note in the harmonic series things start getting pretty badly out of tune with an even tempered scale, so dominant seventh chords don't really include the 7th note in the harmonic series. Even though textbooks may identify that note as the b7 of the fundamental, they only do that because it's the closest note - the 7th note of the harmonic series is actually a little more than 2/3 of the way from the major 6th to the b7th. It's flat by 31 cents.

That applies to the 11th and 13th as well. The 11th in the harmonic series falls almost exactly halfway between the 4th and the #4/b5, and the 13th is a little bit more than halfway from the b6 to the 6th.

Having your ears accustomed to a non-Western temperament (like middle Eastern music) means they might not be as jarring to your ears as they would be to a European or American listener... but they're still so far from our Tertian system of harmony that they're not really going to work for building chords.

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    I suspect that they work just fine for building chords. To my (rather western) ear, at least, the only context in which the harmonic 7th does sound good is building chords. Otherwise it sounds horribly out of tune. – phoog Jun 19 '19 at 18:32
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    ok 12tet minor 7th is about 30 cents sharper than the natural 7th harmonic but to my understanding, the same note on the keyboard implies different ratios in different contexts. If I use v or bIII or biii chords in my song that 7th would be perceived as 9/5. but when I use a I7 chord I think it is perceived as 7/4. Because you can lower your seventh(by tuning a string of a guitar 30 cents lets say) and observe that the dominant seventh sounds more stable. – Ahmet Bilal Jun 19 '19 at 20:48
  • I agree with phoog- the harmonic seventh make a much more consonant sound than the equal tempered minor seventh. I use it a lot in my music. – Scott Wallace Jun 20 '19 at 10:35
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Starting from a just iv chord, with a 6:5 minor third and a 3:2 fifth, consider the other intervals that arise when you add the sixth. A just major sixth would be a ratio of 5:3 above the root; a just minor sixth would be a ratio of 8:5; and you are asking about a ratio of 13:8.

The ratio between the 5:3 sixth and the third is 25:18; the ratio with the fifth is 10:9. The first interval is the inversion of the tritone in a just dominant seventh chord (1:1, 5:4, 3:2, 9:5), so it is somewhat dissonant, but should be tolerable. The 10:9 whole step is of course quite common in justly-tuned music.

The ratio between the 8:5 sixth and the third is 4:3, a perfect fourth, so it is far more consonant. The ratio with the fifth in that chord is 16:15. This is dissonant, but it is a common and pleasant dissonance in just intonation.

By contrast, the 13:8 sixth has a ratio of 65:48 with the third and 13:12 with the fifth. Not only is the first ratio quite distant from the land of simple ratios, but it is also 26.8 cents sharper than a perfect fourth. To my ear, it just sounds wrong: it's not far enough from a perfect fourth to sound like a tritone, but it's much too far away to sound consonant.

If I could hear these intervals in the context of middle eastern music, I might change my tune a bit, as it were. I don't have much experience with such music, but what I am familiar with uses interesting tuning as a feature of melodic expression, not so much harmonic. Perhaps the 13:12 ratio is part of its tonal landscape. If that is the case then this tuning might be well suited to such music.

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  • youtu.be/lVlgMEFu1PI i think you can hear those weird 13/12 intervals in this kurdish/arabic hit. a keyboard solo in maqam husseini. – Ahmet Bilal Jun 19 '19 at 21:25
  • i dont know your ears but those cadences sound really strong to my ears. I am pretty sure those riffs won't work in 12tet. i think there is a structural use of higher harmonics. i mean there are microtonal chords functioning behind. – Ahmet Bilal Jun 19 '19 at 21:32
  • here is a piece in husseini that I put on top of those chords. mega.nz/#!nsczSIzZ!b9sODfaLUx5XBdvkAswo0YppEXk3fZDYuiuX4225p6w – Ahmet Bilal Jun 19 '19 at 21:40
  • by the way note that the ratio 13/11 is slightly lower than 6/5 so in your calculation that 65:48 can be replaced with 11:8. But then we have a bad interval wrt the fifth. So use a third in between 6:5 and 13:11. 12tet minor third works surprisingly well. – Ahmet Bilal Jun 19 '19 at 22:24
  • @AhmedBilâl thanks for the links. Playing a bit with a tone generator, I hear a note at around 0:54 in the first that seems to be in a ratio of 12:11 over the G (around 427.6 Hz). But I do not hear any minor chords, with or without added sixths! I will try to listen to the second over the weekend. – phoog Jun 21 '19 at 22:28

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