Talk:Wolf interval

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[edit] Additions

I've made massive additions to this page, and also corrected errors. These are detailed below.

In music, a wolf interval is an interval between two notes of a scale which is so far from its ideal ratio that it can not be used

There is no such thing as an interval which cannot be used, and "ideal ratio" is left undefined. In fact, in some cases (for instance, the subminor and supermajor intervals which show up in meantone) it isn't clear what the ideal ratio would be, or even if there is one.

If the notes are tuned so that some intervals are equal to or very close to their ideal ratios, at least one interval will be far from its ideal ratio and so be a wolf interval.

This claim is vague to the point of meaninglessness, but to the extent I can interpret it, it isn't true.

In modern Western music the notes of the scale notes are tuned as that all tones are equal and all semitones are half a tone. This makes all intervals slightly out of tune, but usable. There are no wolf intervals.

Badly written and not in all respects correct; I refer to equal temperament now at the bottom, along with well temperaments. In Pythagorean tuning, the interval G#-Eb is such an interval, known as the wolf fifth.

This suggests, incorrectly, that the primary meaning of "wolf" attaches to Pythagorean tuning. In fact, it mainly refers to meantone.

Gene Ward Smith

[edit] Lead paragraph

The lead paragraph took too long to get to the point, and went off on tangents sometimes (it is unneccessary to define a diminished sixth that thoroughly), so I tried to reword it a bit. This is the old version:

If the meantone fifths are tuned from Eb to G#, an anomalous fifth will be the interval from G# to Eb. An interval from G to E is a major sixth; flattening E or sharpening G, and so for instance going from G# to E, gives a minor sixth. The interval from G# to Eb may be regarded as a doubly flattened sixth, or diminished sixth. When twelve notes to an octave are tuned to meantone, intervals in remote keys will sometimes involve augmented or diminished versions of the usual intervals for that chord, with the pitch changing though the keyboard pattern remains identical. Because a diminished sixth used as a fifth supposedly howled like a wolf, it came to be called the wolf fifth.

I removed the definition of a dimished sixth and the explanation of remote keys. - Neonumbers 00:36, 31 Oct 2004 (UTC)

The second sentence of the lead paragraph has become horribly confusing:

The notes that meantone temperament were contra distinctly based around, inherently means that the interval G♯ to E♭ will be this anomalous interval.

What is this supposed to mean? Its grammar is impenetrable, and despite the rest of the paragraph turning blue, it contains no explanatory links at all. For now, I will change it to:

If the meantone fifths are tuned from E♭ to G♯, the anomalous interval will be between G♯ and E♭.

I'm copying the first sentence of the rejected old lead paragraph above, and I'm still not sure what "the meantone fifths are tuned from E♭ to G♯" means, but this is still infinitely clearer than what it is now.

Proginoskes (talk) 20:29, 28 May 2008 (UTC)

[edit] Vorbis links broken

The links to the ogg vorbis files on wikimedia commons are broken. --24.99.22.14 03:56, 15 October 2005 (UTC)

Links are still broken. Rmhermen 04:17, 8 February 2006 (UTC)
I'll make a new example when I have some time. —Keenan Pepper 16:36, 1 March 2006 (UTC)
(Nearly two year later.) In case someone does eventually make new sound files, I've put the associated text in the section Sound files demonstrating the wolf below. --Zundark (talk) 13:09, 16 February 2008 (UTC)

[edit] Citation request

Does anyone have a citation for the remark that the Wolf fifth is named after the howling of wolves? I ask because it doesn't much resemble the howling of wolves to me, so am curious to know whether it was in fact really originally called for this reason or had some other origin and then got this as a later attribution. I know that it is always explained this way but no-one ever seems to back it up with any kind of citation at all, it is just presented as "lore" that everyone knows.

If it was originally named after the howling of wolves of course, probably the best one can expect is to have an early reference to a source that attributes that as the reason for it unless one is lucky enough to trace it back to a primary source that was in print rather than colloquial. Anyway I'm also curious to know if anyone can say how far back the name goes historically and if they explained it in the same way back then.

Robertinventor 01:05, 26 April 2006 (UTC)

[edit] Praetorius on the Wolf F-Ab

One important historical source is Praetorius' Syntagma Musicum of the early 17th century: in the 2nd volume De Organographia he gives a detailed account of meantone tuning. He calls the interval F-Ab or F-G# the wolf, and also says that one might try to move it to Bb-C# or some other places, but in any case it should be left to howl in the forest (which I interpret as meaning, not to be played). This refutes the claim that the term was not historically used for 'subminor' thirds. Praetorius may or may not have recognised that it was close to a just interval, in any case he clearly felt it to be anomalous and undesirable. I suspect the third rather than the fifth was designated as 'wolf' because 17th century musicians would be more likely to try to play a chord of F minor than Ab major. --Tdent 20:49, 7 October 2006 (UTC)

[edit] Zwolf

Since the german word for twelve is Zwolf, I suggest that the discordant twelfth interval derived from this source, not the sound of a wolf.

Oulrich 20:53, 3 August 2007 (UTC)

Do you have a source for this information or are you just guessing because it seems coincidental? I seem to recall reading that the oldest mention of a wolf fifth is in a French text, not German, actually. There is a statement in one of the early chapters of Owen Jorgensen's "Tuning" that mentions a comparison of the beating of the wolf fifth to the howling of wolves, but I don't have the book onhand or I'd quote it to you. - Rainwarrior 03:08, 4 August 2007 (UTC)

[edit] Sound files demonstrating the wolf

I removed the following from the article, as all but one of the sound files has been deleted. I've copied the text here, so that it can easily be replaced if someone makes new sound files. --Zundark (talk) 13:09, 16 February 2008 (UTC)

Wolf_fifth.ogg (33.1KB) is a sound file demonstrating the flat Pythagorean wolf fifth. The first two fifths are perfectly tuned in the ratio 3:2, the third is the Pythagorean wolf. It may be useful to compare this to Et_fifths.ogg (38.2KB), which is the same three fifths tuned in equal temperament, each of them tolerably well in tune.

With meantone fifths running from Eb to G#, the I-IV-ii-V-I cadence in the key of G# major becomes the chord progression G#-C-Eb, C#-F-G, Bb-C#-F, Eb-G-Bb, G#-C-Eb. The Ogg Vorbis file wolf gives this cadence in the key of G# major in a meantone with fifths of 695.838 cents, which is nearly the same as the 2/7-comma meantone of Gioseffo Zarlino. The tonic chord is the wolf triad, the subdominant C# chord is a supermajor triad, the supertonic Bb chord is a subminor triad, and the dominant Eb chord is an ordinary major triad. All four chords of the progression therefore have a different character, and the auditor can make up his or her own mind about the nature of the wolf tonic chord. It is instructive to compare this to the same progression in equal temperament, equal, and in a meantone tuned to G# major, meantone.