<html><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><span class="Apple-style-span" style="font-size: 15px; ">Dr. Dimitar Ninov wrote:</span><div style="font-size: 15px; "><br><div><blockquote type="cite"><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Bach is not so strict with the parallel fifths of unequal size, though. Some theorists consistently call them “unequal fifths” as if they are not parallel and may be used indiscriminately for this sole reason. I am afraid that none of these possible assumptions is true, however. When you move in thirds, you usually say that is a motion in parallel thirds, no matter whether one third is major or another is minor. The same is the case with the fifths. When two parallel fifths (one perfect and one diminished) are perfectly acceptable, they are usually covered by the bass or another voice which moves in parallel thirds and sixths with the voices that form the fifths, such as in the connection I-V4/3-I6 or I-VIIdim.6-I6 with Mi-Fa-Sol as melodic contour. Bach explores these possibilities amply in his compositions. Of course, we also have expansions of this principle.</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Because of this misunderstanding that if two fifths are of unequal size, they may be used just like that,<span class="Apple-converted-space"> </span>sol-fa-mi soprano profile is often harmonized by some musicians with cad.6-4 V7-I, while this harmonization is the least characteristic for that contour and the parallel fifths are not covered in the manner described above. They do not sound very appealing there at all, but “we read somewhere that they are allowed.” In this particular case, it is much better to place this contour and the fifths between inner voices. Otherwise, more typical harmonizations for this soprano are V6-6/5 or V-V6/5 or I6-V4/3-I.</div></blockquote></div><br></div><div style="font-size: 15px; ">This raises several interesting questions.</div><div style="font-size: 15px; "><br></div><div style="font-size: 15px; ">First, I have always taught (and thought) that there is a fundamental difference between P5–d5 and d5–P5 successions: The former contains no approach to a perfect interval and is therefore unproblematic, whereas the latter contains "hidden parallels" and only occurs in certain idioms, such as the ones Dr. Ninov mentions. In particular, I don't think Bach uses the d5–P5 succession between the bass and another voice. Moreover, the idioms involved always (?) seem to have ^7–^4 moving to ^1–^5, whereas a motion from ^2–^6 to ^1–^5 in minor seems to be avoided.</div><div style="font-size: 15px; "><br></div><div style="font-size: 15px; ">HOWEVER, Dr. Ninov's post raises the interesting question whether the P5–d5 succession might also be avoided for some reason (such as "not sounding appealing"). Dr. Ninov, if I understand your post correctly, you suggest that such fifths are generally avoided, but occur in the I6–V4/3–I progression with parallel tenths between ^3^2^1 in the bass and ^5^4^3 in an upper voice. This is an interesting proposition and one that we might ask Prof. Tymoczko to illuminate empirically through his data of Bach chorales.</div><div style="font-size: 15px; "><br></div><div style="font-size: 15px; ">On the other hand, if, for example, it turns out (as I believe it does) that you won't find many cases of cad.6/4–V7–I with ^5^4^3 top voice in that repertoire, that does not yet prove that the reason for this is the avoidance of P5–d5 succession, because there might be alternative explanations. One might suggest, for example, that when resolving the cad. 6/4, ^3–^2 and ^1–^7 motions are more effective in the soprano.</div><div style="font-size: 15px; "><br></div><div style="font-size: 15px; ">In any case, P5–d5 and d5–P5 successions is surely an issue towards which different composers had different attitudes. Incidentally, while Dr. Ninov mentions I–V4/3–I6 as a possibility "amply explored" by Bach, I doubt whether this is actually common at all in Bach's music. I think Bach strongly favors I–VII6–I6, whereas I–V4/3–I6 becomes more common in music by other (later) composers. This, again, is an issue that should be illuminated empirically. Does anyone know occurrences of I–V4/3–I6 in Bach with ^3^4^5 upper voice?</div><div style="font-size: 15px; "><br></div><div style="font-size: 15px; ">Some other examples:</div><div style="font-size: 15px; "><br></div><div style="font-size: 15px; ">Bach: WTC I, A-minor Prelude, mm. 1–2. The voice leading goes from A–E to B–F (P5–d5). Would Bach perhaps have avoided this voice leading in block-chord texture?</div><div style="font-size: 15px; "><br></div><div style="font-size: 15px; ">Bach, WTC II, E-minor Prelude, mm. 60–61. Here we have a rare example of ^4^5 with implied d5–P5 succession, WITHOUT the bass providing the ^3 (VII4/3–I instead of VII4/3–I6). The effect of the fifth is enhanced by its openness (no third at the downbeat). This is clearly an example in which Bach deliberately deviates from norms for creating a special memorable effect.</div><div style="font-size: 15px; "><br></div><div style="font-size: 15px; ">Brahms, Symphony No. 1, Second movement, m. 56. A d5–P5–d5 succession in upper voices.</div><div style="font-size: 15px; "><br></div><div style="font-size: 15px; ">Olli Väisälä</div><div style="font-size: 15px; ">Sibelius Academy</div><div style="font-size: 15px; "><a href="mailto:ovaisala@siba.fi">ovaisala@siba.fi</a></div><div style="font-size: 15px; "><br></div><div style="font-size: 15px; "><br></div></body></html>