Talk:Semitone

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[edit] Rational semitones

I wrote a program to compile a list of all practical rational semitones. That is, all denominators were tested from 1 to 50000, and a new possibility was added to the list only if it was better than the best so far having a smaller denominator. Here they are, with their cents:

  • 1/1 = 0.0
  • 10/9 = 182.40371213406007
  • 11/10 = 165.00422849992202
  • 12/11 = 150.6370585006306
  • 13/12 = 138.57266090392307
  • 14/13 = 128.29824469981426
  • 15/14 = 119.44280826109726
  • 16/15 = 111.73128526977776
  • 17/16 = 104.95540950040728
  • 18/17 = 98.95459223036757
  • 53/50 = 100.87711774616947
  • 71/67 = 100.38951485629148
  • 89/84 = 100.09920982516498
  • 107/101 = 99.90660437922274
  • 196/185 = 99.9940603186754
  • 873/824 = 100.00477973546587
  • 1069/1009 = 100.00281433695989
  • 1265/1194 = 100.0014579802408
  • 1461/1379 = 100.00046554742165
  • 1657/1564 = 99.99970789691965
  • 3118/2943 = 100.00006290886779
  • 4775/4507 = 99.9999397141372
  • 7893/7450 = 99.99998838019101
  • 11011/10393 = 100.0000094845786
  • 18904/17843 = 100.00000067284903

With a denominator smaller than 50000 there is nothing better than 18904/17843, apparently. I'm not sure when the next best one is. Anyhow, the list is smaller than I expected it to be. It might be worth including? I dunno. - Rainwarrior 05:44, 20 September 2006 (UTC)

Obviously, you are a computer whiz! I personally find it intruiging. But I think it might be "pushing the point" a little too far...the article is about the semitone...this is "pure math". If the average reader has even one reasonable approximation, the idea is conveyed. No offense, but I'd rather not see it in the article. (In fact, doing so could lead to similar lists for all the intervals!)
Anyway, what do you think of just removing the present 196/185, along with it's reference to the Hammond organ? Prof.rick 06:03, 20 September 2006 (UTC)
Hold on! Your 89/84 rings a bell! I feel sure I've come across it as a practised semitone, somewhere. I will start checking some resources now. Prof.rick 06:07, 20 September 2006 (UTC)
Sorry, no luck...can't find a reference to 89/84. I guess I imagined it. Prof.rick 06:24, 20 September 2006 (UTC)
I went ahead and removed 196/185, and the Hammond reference. (If you disagree, it's easy enough to put back.) Personally, I think this short list of "approximations" is just the right length to be proportional to the article as a whole. Let me know what you think. Prof.rick 06:33, 20 September 2006 (UTC)

[edit] A nice article!

Looking over the article in it's entirety, I am quite happy with it. Of course, future improvements can be made, but I think, as it stands, it is complete but not excessive, intelligently presented, and attractive in it's layout...well worth the time we have invested.Prof.rick 06:54, 20 September 2006 (UTC)

I've taken this opportunity to archive the talk page. - Rainwarrior 21:07, 20 September 2006 (UTC)

Great! I'm sure we'll meet again on another article. Cheers, Prof.rick 00:31, 21 September 2006 (UTC)

Yes - a great article. Well done to both of you. Thanks, Prof for your kind words on my modest contribution, and I look forward to further collaborative efforts in future. (Mark - 21 September 2006)

Thank you, Mark! Please, don't underestimate your contributions! They were absolutely vital to the final product.

Re article, "Augmented Unison": changed "regardless of harmonic underpinning" to "independent of harmonic underpinning", since chromatic passages often appear unaccompanied by chords, especially in the Classical period. ("Regardless" might suggest some harmonic back-up is present, while "independent" leaves the matter wide open.)

And to you, Mark, I am sure we will meet again on another article!Prof.rick 04:25, 22 September 2006 (UTC)

I changed independant to "regardless" for that very reason. Chromatic scales very (very) frequently cut right across chord progressions in classical music and are not part of the harmony. - Rainwarrior 07:25, 22 September 2006 (UTC)

No problem. (It's really a matter of semantics rather than musical concepts.) I changed it back to "regardless". Prof.rick Sept. 22 2006

Rain, I noticed on your list of approximations, the denominators are 9 17 inclusive...then a large gap to 50! I think this is a very valid reason for your inclusion of 18/17, and a reference to it's use. (Funny, these ratios behave with the same unpredictability as prime numbers!) Prof.rick 05:33, 22 September 2006 (UTC)

Rain and Mark, I have been questioning the description of the Chopin "wrong note" Etude. This is such a subjective matter, as we try to pinpoint the "character" of the music in words. As well as humorous, I find it rather sardonic, even sinister! (Whenever I perform it, I am well aware of that "touch of evil"!) However, before changing the article, I would like your views. Prof.rick 02:34, 24 September 2006 (UTC)

Sorry, Prof. I'm not familiar with that etude (shameful, I know). However, it's mentioned elsewhere in Wiki at Chopin etudes where the effect is described as piquant rather than humorous. As you say, it's subjective. Maybe you could find a word that no-one can disagree with, such as 'striking'. (Mark - 24 September 2006)
I figured that the nickname itself is grounds enough to call this "humour". Of course your personal reaction to the sound is subjective, but I think this fits its general perception, and probably the composer's intent. This kind of dissonance, unprovoked, and unprolonged, is by no means typical of the style; it's meant to stick out, it's clumsy (especially for the player).
But, if you were going to change "humourous" to "striking" or "piquant" on the grounds that "humour" is too subjective, we're losing a lot of description. "Striking" says nothing about the character of the gesture, it would make the whole paragraph seem more or less useless to me. - Rainwarrior 16:15, 24 September 2006 (UTC)

I have to agree with Rain...the term "striking", for example, says little about the "character" of the music. I certainly agree with "humorous", but believe there is inherently more in this musical instance. (Consider how Liszt, for example, used the semitone, with a brief non-chord tone [semitone] in the opening of the "Mephisto Waltz" to convey an evil essence! It can certainly express a sinister element. "Mischievous" strikes me as an apt descriptive term. What about "humourous, yet rather mischievous"?" ("Wrong note" even suggests that somebody is "doing something wrong"...i.e. is "up to no good"! (Literally, dissonance can suggest "wrong", whether we interpret the word to mean funny [clumsy] or sinister.)

I am considering two other factors. First, this theme appears in a minor key, possibly lending a flavour of "darkness" or "spookiness". Second, compare it to the contrasting middle section...it may offer a clue. (Does the melodious mid-section offer a contrast primarily to humour or to "mischief"? I can't help but feel that it does both, but is a wonderful specimen of typically Chopinesque "soul-cleansing".) "Humourous, but naughty" or "humorously naughty", also occurred to me.

It might seem we are dwelling on a relatively minor point, but in the interest of doing our very best with this article, I think it's worth that extra bit of effort. (Mark...could you arrange to LISTEN to this Etude, then let us know here how it strikes you? This might help us reach a final decision on the description.) Prof.rick 19:48, 24 September 2006 (UTC)

Does anyone also find a sarcastic element in this Etude? (It remind me a bit of a little kid, sticking out his tongue...a rejection of "authority" or "expected behaviour". (Sassy!) Prof.rick 19:58, 24 September 2006 (UTC)

Well, in the Mussorgsky it's an obvious reference to chirping. In some of the music for the video game Super Mario 3, it gets used for a similarly "cute" effect. In Liszt's Mazeppa etude, it always strikes me as a very clumsy ride. In this Chopin Etude, it sounds to me deliberately annoying, like a joke (and not unlike laughter). It's also kind of weird how little time is actually spent in E minor in this piece. I dunno, what do you want to call this effect? - Rainwarrior 20:43, 24 September 2006 (UTC)
I only suggested 'striking' as an example of a less subjective term, not necessarily descriptive of that piece, which, as I said, I don't know. There's no need for me to listen to it as we can't allow my subjective appraisal to influence the description. Find another more appropriate term - or use "humorous" if the piece is known for its humorous effect. But be careful. Chopin may have used the semitone to humorous effect in that piece, but I'm sure he could have used a whole range of intervals to equally humorous effect. Don't dwell on this or you'll be in danger of giving the false impression that semitones are intrinsically funny - and then someone will come along quoting the 'Jaws' theme in protest. (Mark - 24 September 2006)

I agree, Rain, in the Moussorgsky, it is a reference to chirping, rather than humourous. Regarding the Liszt Mazeppa, I find it clumsy,and deliberately annoying, to say the least, and add "rude" and at times almost brutal, domineering, and even sadistic...definitely evil! Regarding the Chopin Etude, I have also thought of "mocking" or "teasing". A pianist-friend also added "frolicking", agrees with both "humorous" and "sinister" but added the valuable term, "unsettled". (By the way, I wonder who named this the "wrong note" Etude? Surely we can't simply acccept one text-book definition. Without success, I consulted five different books on the works of Chopin, and found no descriptions of this Etude! (Maybe if we look at the broader meaning of the word "wrong"...I dunno.) If you think of music as "a living thing", and is therefore subject to "character change" as it progresses, then the fact that this exerpt has much material in the major key is not very signicant. Chopin often makes the major-minor change freely. However, It is the FIRST instance which sets the tone for the piece. (Consider, for e.g., the Fantaisie-Impromptu, "A" section. It begins in the minor, giving it a very serious nature, but also has substantial sections in the relative major. The tonality of the opening is the most critical is "setting the stage", I think. (Rain, on the other hand, I have also used acciaccatura semitones in my own compositions to convey a carefree escape from the harsh realities of life, the sublime, the heavenly.)

Mark, why can't we let your subjective appraisal influence the description? You've made a very important point, particular with reference to "Jaws"...the minor second can serve a wide variety of expressive possibilities. You have raised a VERY important point...we do NOT want to give the impression that semitones are inherently funny!

Why don't we all re-read this section of the talk page, and make a list of the possible adjectives...then narrow it down. I would begin by removing "jocular", and "whimsical" which were used in the article (Of course, the question arises: are we trying to describe one musical specimen, or the "musical disposition" of the semitone?) I also like the word "striking", but feel we should be more specific. Maybe we should make a list on this page, then vote on it. Prof.rick 02:54, 25 September 2006 (UTC)

"Itchy?" Prof.rick 03:17, 25 September 2006 (UTC)

Whatever description we arrive at, I think we should use a term such as "might be described as", rather than stating a subjective matter as though it were unquestionable fact (e.g is humourous). Also, the use of two or three adjectives might help, but not the existing three, which are too much alike to convey this musical paradox. Prof.rick 03:23, 25 September 2006 (UTC)

Rain, referring to the major/minor element, I would also like to point to the first Chopin Waltz (Op. 18). The B-flat minor section also makes use of acciaccatura semitones, (as well as some other intervals) (bars 133 - 148)for a specific purpose in the overall structure. All along, the piece has been so jubilant, and in major keys. So often in every art, a "conflict" somewhere along the line is employed, to "play up" the sublime, serene, or joyous sections (or vice versa!). The fact that this passage is written in a minor key seems to suggest that it is IS the "conflict" section. (Which of course, suggests that Chopin was well aware of the element of conflict which the semitone can convey.)

Also, I had previously given you examples of Chopin's use of the harmonic augmented unison in one Ballade, and the Berceuse. You can also find it in the 8th Nocturne, Op. 27, No. 2 (bar 13). (And it each of the 3 Chopin instances I have quoted, the effect is hauntingly beautiful and ethereal.) The point is: I am wondering if the Liszt Etude is the best example of a harmonic augmented second, since it's use there is defiant and very dark, even ugly...yet in the Chopin examples, it is literally "a breath of heaven". What do you think? (We know that sounds which are displeasing in the bass might be quite delicious in the high treble, corresponding approximately to the "spacing" of the harmonic series.) Prof.rick 04:53, 25 September 2006 (UTC)

Mark, although you have far less to say that either Rain or I, your comments are always well-thought, and have been indispensible. Often, a one-on-one difference of views seems insoluble...the voice of a knowledgeable third party (especially one with your particularly astute and unique insight) can help bring about a final "answer". We NEED you!!! Following is a list of some of the adjectives so far mentioned, to describe the semitones in that Chopin Etude (and I DO hope you can find an opportunity to listen to it...playing it is one matter, but to interpret it's musical statement requires only open-minded listening). Here is the list:

humorous, whimsical, jocular, sardonic, sinister, naughty, mischievous, striking, piquant, defiant, sassy, itchy, clumsy, rude, mocking, teasing, frolicking, unsettled. (Add more, if you wish.) If we can narrow it down to 2 or 3 agreed adjectives, we've won!

I won't express my own proposal yet, but wait to hear what you, Rain and Mark, have to say. However, we must keep in mind that music is a language unto itself; therefore, our verbal descriptions are inherently both subjective and inadequate...it's something like trying to teach the Russian language, using only French. (Just one musical phrase can "say" many different things, hinging on the listener, and his mood/disposition at the time of listening.) But ultimately, we must ask, what, to the best of our knowledge, was the composer's intention.

Chopin is SUCH a complex character, full of wit, and even a "mimic" of others. (Apparently, he could he even contort his facial muscles to "look like" the person he was impersonating!)

PS: Judging by spelling and grammar, are we all Canadians? Prof.rick 06:08, 25 September 2006 (UTC)

I thought we were all Brits.
Prof - "If it aint broke, don't fix it". I just had another read of that paragraph and it's FINE. "Eccentric dissonance" is a great phrase. Let anyone argue with that if they dare. "Humorous" and "whimsical" are fine too, (Maybe "jocular" is pushing it a bit). As Rain said, its nickname suggests that it's known for its humorous effect, so I don't think you're being subjective in using that term. For style purposes, two phrases I would suggest changing are "...used for a humorous effect" to "...used to humorous effect" and "...which contrasts with a more lyrical middle section" to "...which contrasts with its more lyrical middle section".
The first change makes it sound a little more encyclopedic and the second change reminds us the main topic is the semitone, not the Chopin piece. Somehow using "a lyrical middle section" sounds like we've shifted the main focus from semitone to the etude's lyrical section. (Mark - 25 September 2006)
I like Mark's suggestions. Make whatever amendations you think are appropriate. I like the idea of making the opening sentence more general. Maybe start with something more like: "In unusual situtations, the minor second can add a great deal of character to the music. For instance, in Chopin's..." and then discuss this specific one? As for the nickname, I don't know who came up with it (a lot of 19th century critics liked to give nicknames to pieces... if I had to point a finger, I'd probably point at Eduard Hanslick), but I've seen it in a few places. - Rainwarrior 01:48, 26 September 2006 (UTC)
And BTW, I am a Canadian, yes. It says so on my user page. - Rainwarrior 01:50, 26 September 2006 (UTC)

Actually, I though we were all French Poles. Re:"if it ain't broke...": In a sense it was broke, possibly implying that all semitones are humorous, a point previously made by Mark. I admit, I've been thinking about this matter all day. Semitones can also be very sensuous (e.g. their use as grace notes in jazz and blues). Obviously, we cannot list all the expressive possibilities of the semitone. I also like Mark's idea, and yours, of starting with an opening sentence which "leaves the door open", and I like the "for instance", as the reader will understand that "humorous" does not necessarily apply to all semitones. I'm satisfied. I'll leave the edit to your discretion. (Man, this is a great article!!!) Prof.rick 03:29, 26 September 2006 (UTC)

And I LIKE the phrase, "eccentric dissonance". HA! Prof.rick 03:34, 26 September 2006 (UTC)

Rain, I've used your introductory sentence (re character of the minor second), and moved "humourous" to replace jocular. (Of course, you can change it back if you like!)

Mark, I'm also following your suggestion: change "used to humourous effect" and "which contrasts with a lyrical middle section". Prof.rick 22:14, 28 September 2006 (UTC)

Sorry, Mark! I re-read your comments, and replaced a with its. Hope your find these minor edits OK. Prof.rick 22:45, 29 September 2006 (UTC)

[edit] The Minor Second is back!

I was quite surprised that vandalism had corrupted this article on Nov. 28/06. An attempt was made to recover the page, but somehow the Minor Second (item 1 of the Contents) had vanished! I have tried to restore it, using "copy and paste" from the History. I hope this has not caused any unnecessary problems. (Future edits were preserved).

Please, when ANYONE (especially those anonymous IP editors) want to make edits to any article, it would be appreciated if you'd leave a note on the Discussion Page, mentioning your reasons for change. Some of us invest a great deal of time, effort, research, discussion, and scrutiny...to arrive at the most complete and accurate articles possible. Prof.rick 10:36, 16 January 2007 (UTC)

Hi Prof Rick. I completely missed the vandalism, probably because it was an accident. It looks like Di4gram (talk · contribs) was reverting other vandalism which replaced the section with jibberish and forgot to replace the original material there, so I guess I thought the vandalism had been taken care of, but it hadn't. Anyhow, it looks fine now. Thanks for correcting that. - Rainwarrior 05:17, 17 January 2007 (UTC)

[edit] Editing augmented unisons

Hi Rain, Hope you don't mind...I have edited out your use of diatonic semitones to notate a chromatic passage: e.g. C, Db, Ebb, Fbb, Gbbb, etc. I feel this particular point is irrelevant...it may suggest that the chromatic semitone is a "necessary compromise". (How often have you come across a triple-flat?) Obviously, both composers and readers prefer the most direct route, e.g. C, C#, D, D#, E, and think in such terms. I don't believe the use of chromatic semitones needs to be justified. (Of course, if you disagree, you can restore your example.) Best, Prof.rick 07:41, 21 January 2007 (UTC)

[edit] i thought the tritone was the most dissonant interval

i'm no harmonic scholar, but it seems that the tritone is always dissonant, whereas the semitone is only sometimes dissonant. to my ears the tritone always sounds far more difficult. 67.172.61.222 22:52, 9 March 2007 (UTC)

Taken out of context (a musical context) it seems hard to say what is more dissonant. In any case, the article's opening statement of the semitone being "the smallest interval commonly used in Western music, and is considered the most dissonant" -- it would be nice to have a reference (ie, who says it is the most dissonant?), and/or some kind of note about what method of measuring dissonance results in the semitone being the most. The dissonance pages makes it clear that the term is used variously, with differing ways of measuring. Pfly 02:52, 13 March 2007 (UTC)
The tritone appears in every dominant seventh chord; it is extremely common. The minor second on the other hand is used quite sparingly, harmonically. This speaks to its relative dissonance in a way. The simplest just ratio for a tritone is 7/4 whereas it is 16/15 for the semitone, which is a more complicated ratio, which is one way to quantify dissonance. There are other arguments though, you could make the argument that the tritone has a greater implication for resolution than the minor second (because of its place in the dominant seventh chord), and if your definition of dissonance is a tension that leads to resolution (which is a different way of qualifying dissonance), it's could be reasonable to say that the tritone is more dissonant. All in all, I'd say statements like "most dissonant" aren't terribly useful anyway, given how various the definitions of dissonance are, but by most usages, the minor second is the more dissonant. - Rainwarrior 05:43, 13 March 2007 (UTC)
a dominant seventh chord sounds, without any surrounding context, fairly dissonant to my ears, at least quite tense. i think the best measure of dissonance, as a totally subjective concept, is the ability of an interval to sound "natural", which the tritone, quite simply, never does. listen to "From the Morning" by Nick Drake if you want a good example of a semitone used as an interval. if you try to write a piece on any instrument that includes a tritone, good luck making it sound that melodic. by a more meaningful measure of dissonance, a tritone divides the octave exactly in half, creating a lack of a tonal center in just two notes. lastly, just play a semitone as two individual notes, and then do the same for a tritone. you'll find that going from E to F sounds much different than E to A#. 67.172.61.222 00:47, 16 March 2007 (UTC)

[edit] Diatonic and chromatic

The article uses the terms "diatonic" and "chromatic" without adequate explanation. These terms cause serious uncertainties at several other Wikipedia articles, and in the broader literature. This is amply demonstrated in discussion above, and in the archived discussion. For example, some take the term "diatonic scale" to include all of the minor scales, and they have justification for this usage in published sources. One example will suffice. User Prof.rick writes, in Talk:Semitone/Archive_2:

The problem with referring to "diatonic steps" could present a possible source of confusion to first-level theory students. (What does "diatonic" mean? Which kind of diatonic scale? Major? Natural minor? Harmonic minor? Melodic minor?) This seems to be an easier way to define a minor interval, in terms the average first-level theory student can readily grasp.

This is not an aberrant or isolated understanding of the term "diatonic" by any means, but it is inconsistent with the article Diatonic scale; and that article itself comes close to being internally inconsistent. It certainly would be misleading to the reader seeking clear and current definitions. Some of us thought that both "diatonic" and "chromatic" needed special coverage, so we started up a new article: Diatonic and chromatic. Why not have a look, and join the discussion? Be ready to have comfortable assumptions challenged!

– Noetica♬♩ Talk 22:14, 3 April 2007 (UTC)

[edit] Phi Semitone

To Dicklyon:

No, you will not find the Phi semitone described directly at the references I provided. However, at the "Elliott Sharp" page, check the discography. Find "String Quartets 1986-1996 (2003)". Read the CD insert. Would you like it mentioned in the article? If you're not satisfied, feel free to remove the Phi semitone, by all means.

Your aggressive approach could certainly be used at "Mathematical Coincidence", which still has a ton of garbage. I corrected the expression of 1/81. Rather than removing it, I've called for discussion. Also, "Golden Ratio" still has a lot of it, too. Prof.rick (talk) 01:46, 15 January 2008 (UTC)

OK, I'll take it out then. I agree the 1/81 should go, but I saw you were headed that way, so didn't see a need to get involved. As for golden ratio, I do keep after junk there; feel free to point out any you notice that I missed, or fix it yourself. Dicklyon (talk) 03:59, 15 January 2008 (UTC)

Dick:

Reverted to the Phi semitone version, pending your reading of my comments regarding source, and possible discussion by other editors. Prof.rick (talk) 07:06, 15 January 2008 (UTC)

No problem. While we're waiting, why not go ahead and add a citation to that CD insert, with a quote, so we'll know what it says. Dicklyon (talk) 07:19, 15 January 2008 (UTC)

Reference to Elliott Sharp's String Quartets removed. Prof.rick (talk) 00:06, 16 January 2008 (UTC)

As one of the two principal writers of the Semitone article (which required many weeks of exhaustive research, organization, etc.) I admit we had agreed to keep the section on "approximations of the tempered semitone" brief and relevant. I have therefore removed any mention of the Phi semitone. The information is trivial, and simply doesn't warrant extended quotes from CD inserts. Prof.rick (talk) 01:50, 16 January 2008 (UTC)