Talk:Harmonic seventh

blues seven and flatted seven

Musician Ellen Fullman says these terms are equivalent to harmonic seventh:

• "The harmonic seventh interval in just intonation is known popularly as the blues seven,or flatted seven."

Ellen Fullman, "The Long String Instrument", MusicWorks, Issue #37 Fall 1987

(The WP article, Blues, cites Fullman, but the link to the PDF file is dead. This link is to the google cache.)

• "The naturally occurring seventh partial in the harmonic series is flatter than the seven in equal temperament. This interval is known to musicians as the blues seven."

Ellen Fullman & Kronos Quartet Perform at Other Minds 8, 2002 (March 9, 2002)

--Jtir (talk) 19:07, 17 July 2008 (UTC)

Out of curiosity, I checked Grove (1980). The entries for "Harmonic seventh" and "Blue note" say no such thing. --Jtir (talk) 18:52, 19 July 2008 (UTC)

Merge with minor seventh

Should this article be merged with the minor seventh article? It seems to me that the harmonic seventh is just the most consonant version of the minor seventh.Composerjude (talk) 16:56, 23 February 2009 (UTC)

In just intonation, they are two different notes. One is an interval of 7/4 and the other is an interval of 9/5. In the 12-tet system, there is one note that is nearby to both of them (the minor seventh), and it's frequently used for both of them. But that doesn't *really* mean it's the same note. People using 12-tet approximate two different harmonic concepts using the same note, that's all. And frequently when used in a major context people do play the note "flat" to more clearly indicate the harmonic seventh.2601:140:8980:106F:E404:599F:C40C:7035 (talk) 04:00, 4 August 2018 (UTC)

49 cents

Composer Ben Johnston uses a small "7" as an accidental to indicate a note is lowered 49 cents

This is confusing. I suppose the point is that the harmonic seventh is 49 cents lower than 9:5. Based on the first sentence, the reader will wonder why the "7" doesn't mean 31 cents lower. I had to do some calculations to figure this out. 68.239.116.212 (talk) 04:24, 24 December 2009 (UTC)

How is that fairly direct statement confusing? "Based on" which "first sentence" (the first of the article, paragraph, or the sentence directly preceding)? Hyacinth (talk) 13:12, 24 December 2009 (UTC)

Figured out and explained. Hyacinth (talk) 10:43, 26 December 2009 (UTC)

Contradictory Logic

This article defines the subject note as a relative 9.7 semitones while also stating that it is 1000 cents in the equal temperament. One of these statements must be false because they contradict each other. To exemplify, this logic is not consistent with the layout of the page pertaining to the inverse note, which states its inverse note as equally tempered to 200 cents and thus 2 semitones.

I believe this Harmonic 7th page was meant to have its equal tempered cents to be ~969 and its just intonation cents at 1000 due to this note being non-native to the modern chromatic scale. However, this would mean that the inverse note's page and a few others would have to be changed. If not, then this current page should have the 9.7 semitones in the top right box changed to 10 so that it is consistent with the page of the note's inverse. — Preceding unsigned comment added by 76.17.131.250 (talk) 21:00, 11 August 2014 (UTC)

Say what? Intervals in (12 tone) equal temperament are always a multiple of 100 cents, by definition; and 1000 cents cannot be a just interval. (Well, 55:98 is 1000.02 cents, but I'm guessing that's not of interest here.) —Tamfang (talk) 04:55, 22 August 2014 (UTC)

This article states that the equal tempered equivalent of the harmonic seventh is 1000 cents (it approximates it with the same interval as the minor seventh). Tne article on the septimal whole tone (the inverse) states that its equal tempered equivalent is 200 cents (it approximates it with the same interval as the whole tone or major second). Those add up to 1200 cents, an octave. The math checks out. The approximate "number of semitones" is just so that readers can get a sense of where the harmonic seventh proper (justly tuned, the octave equivalent of the 7th harmonic) falls in relation to more familiar equal tempered intervals. — Gwalla | Talk 18:06, 22 August 2014 (UTC)

Barbershop intonation

This paragraph bothers me:

Some theorists[who?] believe that the harmonic seventh is also used by barbershop quartet singers when they tune dominant seventh chords (harmonic seventh chord), and is an essential aspect of the barbershop style; however this claim was not supported by the empirical data of Hagerman and Sundberg (1980), and the failure of other psychological studies on intonation to find evidence for the harmonic seventh casts doubt on its musical or psychological existence. Instead, Hagerman and Sundberg found that tuning of major and minor third intervals in barbershop lies between just (4:5, 5:6) and equal temperament.

The claim is not totally ridiculous, but there is a lack of citations. Intuitively, one would think that the 7:4 harmonic seventh, which is a simpler ratio and which therefore beats more beautifully than 9:5 minor seventh, would be an instinctive choice for singers with diligent intonation. I also do not understand how there could be any doubt about the "musical or psychological existence" of the harmonic seventh - even if it never appears in barbershop music (a claim of which I am highly skeptical anyway and would maybe even say is flat out untrue because I believe I have heard this type of intonation many times). Furthermore, the claim that any barbershop quartet would purposely tune the thirds of major triads in any other ratio than 5:4 is ridiculous. The whole point of the music is the juicy sound of pure harmonies - it may be and often is the case that the singers sing with slightly inaccurate intonation and either fluctuate or fail to correct the tuning, and it may also be that major thirds in chords other than major triads may be tuned differently, but it is misleading to conclude from that that the tuning of these intervals always lies between just and equal. You don't need measuring equipment to check that, major triads in barbershop music are clearly not supposed to (otherwise, why is the music sung without vibrato?) and don't often have dissonant beating. — Preceding unsigned comment added by BridgeTheMasterBuilder (talk • contribs) 23:05, 13 May 2017 (UTC)

Agreed, even if the statement on barbershop music is accurate (possible, but still a grand claim), the following quote "failure of other psychological studies on intonation to find evidence for the harmonic seventh casts doubt on its musical or psychological existence" is just plain ludicrous. It's so difficult to even interpret what that is *supposed* to mean, as it's so patently untrue. — Preceding unsigned comment added by 92.28.93.182 (talk) 16:40, 21 October 2017 (UTC)

Mathematical error

"The harmonic seventh differs from the Pythagorean augmented sixth by 225/224" This is false. The pythagorean augmented 6th is 59049/32768, and 7/4 differs from this by 59049/57344, a rather large 51¢. The pythagorean augmented 6th is a very obscure interval, and not of much interest musically. I believe the intent of this sentence is to discuss a different augmented 6th interval, the one that actually does fall within 7.7¢ of 7/4. This is 225/128. That's the interval from a minor 2nd of 16/15 up to a major 7th of 15/8. So I suggest changing "Pythagorean augmented sixth" to "5-limit augmented sixth of 225/128", or else making the more general statement that every common septimal ratio is only 7.7¢ away from some 5-limit ratio. SeventhHarmonic (talk) 00:24, 9 April 2020 (UTC)