Talk:Septimal minor third

Added audio

I added two audio files of synthesized sounds. Please let me know what you think...there's a lot of flexibility in creating the sound files, and I'm not sure if I got the appropriate lengths of time, timbres, etc. I figured that pure waves are more likely to have accurate pitches, which is why I used them instead of actual samples which have more overtones and may have varying pitch. Cazort (talk) 14:49, 9 January 2008 (UTC)

They are high pitched and harsh, at least on my system. Hyacinth (talk) 01:55, 6 August 2008 (UTC)

I agree. Cazort (talk) 03:25, 30 August 2008 (UTC)

Request

I would like to request for someone who knows about this sort of thing to add some material to this page and to the other septimal intervals: septimal major third, septimal whole tone, etc., about the occurrence of these intervals in music. Cazort (talk) 03:25, 30 August 2008 (UTC)

Comparing consonance of minor triads

"The septimal minor third has a darker but generally pleasing character when compared to the 6/5 third. A triad formed by using it in place of the minor third is called a septimal minor or subminor triad; however in fact that chord is a part of the overtone series, or in other words is an otonal chord, with ratios of 6:7:9, whereas the ordinary minor third [sic] is a utonal chord. While the septimal minor third is classed as a 7-limit interval, and the septimal minor triad as a 9-limit chord, the fact that the chord is otonal makes it sound perhaps about as consonant as the just minor triad."

The author probably meant to say "ordinary minor triad" instead of "ordinary minor third".

It may be unproductive to explain consonance based on otonality vs. utonality. The ordinary minor triad, assumed above to be utonal, is otonal too, found in the overtone series at 10:12:15 (and infinite higher locations), with a lowest wide-voicing occurrence at 3:5:15.

It may be unproductive to explain consonance based on complexity limit. 6:7:9 ranks less complex than 10:12:15 in odd-limit, but more complex in prime-limit.

I propose a syntax of "7-prime-limit", or "7-odd-limit", instead of "7-limit", which can be ambiguous.

-- Another Stickler (talk) 11:15, 5 October 2008 (UTC)

Harmonic series

Since I have sourced and quoted the information I have added to the article you actually need to find a source to support your position before you revert my edits. Hyacinth (talk) 17:44, 21 July 2009 (UTC)

Note that the book cited is not by Harrison, but by Miller & Lieberman and titled Lou Harrison. Hyacinth (talk) 17:46, 21 July 2009 (UTC)

No, you source, but you translate the content wrong with your own words. Answer my questions to clear things out. What's the frequency of a septimal minor third if the fundamental is 600 Hz? And what is the frequency of the seventh harmonic and what is the frequency of the sixth harmonic? If you answer this properly we can reach an agreement. If you don't know the answer, no problem, I can help you with it, but the answers of these questions points out your assumption is wrong.83.87.74.107 (talk) 18:22, 21 July 2009 (UTC)

Where did I say the 7:6 septimal minor third "is between 7/6 and 6/5"? Hyacinth (talk) 18:27, 21 July 2009 (UTC)

AHA! Now are we getting somewhere (I just read your edit in the article). You confuse the Minor seventh and Major seventh, with the seventh harmonic. The seventh harmonic I am talking about is the 6th overtone (if the fundamental is 100 it is 600 Hz). You mention the harmonic seventh instead of the seventh harmonic, which is something completly different. Can you follow me? The serie prime, second, third, fourth is musical theory (Western). What I mean with 1st, 2nd, 3rd harmonic are the overtone series. These are physical facts. The harmonic seventh is inbetween the major sixth and the minor seventh. The septimal minor third is inbetween the major second and the minor third. Both tones are consonant with eachother (ratio 6:4) 83.87.74.107 (talk) 18:33, 21 July 2009 (UTC)

Give me a minute about your q above concerning the 7/6 and 6/5. I'm going to reread the article accuratelly if it is now correct. Hang on. 83.87.74.107 (talk) 18:33, 21 July 2009 (UTC)

I doubt if people still understand the point of this inclusion. But what's written now is correct. 83.87.74.107 (talk) 18:37, 21 July 2009 (UTC)

I'm done for now, Can you check if you understand this version? —Preceding unsigned comment added by 83.87.74.107 (talk) 18:43, 21 July 2009 (UTC)

See the following image from Harmonic series (music):

An illustration of the harmonic series as musical notation. The numbers above the harmonic indicate the number of cents it deviates from equal temperament. Red notes are sharp. Blue notes are flat.

Hyacinth (talk) 18:46, 21 July 2009 (UTC)

You did not take the time to follow the link to harmonic seventh, which was provided because seventh harmonic redirects there and for good reason. It is a coincidence that the seventh harmonic forms a seventh with the fundamental, thus being called the harmonic seventh, but despite this coincidence it is still both a seventh and the seventh harmonic. Hyacinth (talk) 18:53, 21 July 2009 (UTC)

I was allready typing sorry: I know this yes. What's exactly your point? The 7:6 is not in this serie as shown above, it is the 7:1 (the blue dot with the notification of '-31'), and that's the 700 Hz if the fundamental is 100. Transposed back in steps to the first octave it is 350 -> 175Hz. The octave is 200. So the Harmonic Seventh of 175 Hz is inbetween the major sixth and the minor seventh. The harmonic seventh is in that case 7:4. 350 was 7:2 (the harmonic seventh in the second octave interval. The 7:3 is the septimal Minor third in the second octave interval and the 7:6 is the septimal minor third inbetween the first octave interval appearing inbetween the 2nd and the 3rd fret. The anomaly 7:5 is pretty near the 6th fret (it is the harmonic tritonus) 83.87.74.107 (talk) 18:59, 21 July 2009 (UTC)

And now an answer to your reply :You did not take the time to follow the link to harmonic seventh. There appears to be conflict within the terms and how to call things. If you are taking it from the Western musical theory you are right, if you take it from a logical linguistic rule the seventh harmonic is 6x the freq of the fundamental and indeed a harmonic seventh accidentally with the again the word seventh. To avoid this problem it might be good to call the harmonic an overtone (which is the 6th overtone) and call the harmonic seventh a harmonic seventh and never use the term seventh harmonic in this particular subject to avoid unlogical texts. Are you with me? 83.87.74.107 (talk) 18:59, 21 July 2009 (UTC)

7:6 does exist in the series shown above, as the relationship between 7:1 and 6:1. Hyacinth (talk) 19:05, 21 July 2009 (UTC)

Now you mention something I haven't thought of before. You are right. A difference tone appears when you play 700 and 600 Hz. But that's 100 Hz and I don't see the 7:6 in it. where do you think this ratio is? Note that there is a difference of notation again within 7:6. That's not a frequency ratio causing a septimal minor third, but it a chord ratio. 83.87.74.107 (talk) 19:09, 21 July 2009 (UTC)

The 7 is a septimal minor third of the 6. Not of the fundamental tone. 83.87.74.107 (talk) 19:11, 21 July 2009 (UTC)

There is no "logical linguistic rule" that the seventh harmonic is six times the frequency of the fundamental. Hyacinth (talk) 19:14, 21 July 2009 (UTC)

The sixth overtone (I avoid the term seventh harmonic if you don't mind) is for sure six times the freq of the frequency. Why are you doubting that aspect?

I'm coming to the conclusion we are both talking about totally different things and are confusing eachother since both options share many of the same terms, but within a different context. This is pretty difficult to solve. I don't know how to write this down properly from Western musical perspective, only from the pov of physics.83.87.74.107 (talk) 19:17, 21 July 2009 (UTC)

This was quiet a discussion. Thanks a lot. It's all clear for me now. Have a nice day:) 83.87.74.107 (talk) 19:28, 21 July 2009 (UTC)

The first overtone/second harmonic is twice the frequency of the fundamental. Thus the sixth overtone/seventh harmonic is seven times the frequency of the fundamental (see Overtone#Musical usage term). Hyacinth (talk) 19:50, 21 July 2009 (UTC)

I agree, perhaps somewhere I made a miscalculation, but this was exactly my point. The confusion lies within prime, min/maj second, min maj third vs first, second third overtone. It's all clear for me now how you translated the cited source. 83.87.74.107 (talk) 07:34, 22 July 2009 (UTC)