is difficult to say which I like best,” replied Heller, “for I like them all; but if I were pressed for an answer I would probably say the one in A minor.”  This gave Chopin much pleasure.  “I am glad you do,” he said; “it is also my favourite.”  And in an exuberance of amiability he invited Heller to lunch with him, an invitation which was accepted, the two artists taking the meal together at the Cafe Riche.  The third waltz (in F major; Vivace) shows a character very different from the preceding one.  What a stretching of muscles!  What a whirling!  Mark the giddy motions of the melody beginning at bar seventeen!  Of this waltz of Chopin’s and the first it is more especially true what Schumann said of all three:  “Such flooding life moves within these waltzes that they seem to have been improvised in the ball-room.”  And the words which the same critic applies to Op. 34 may be applied to all the waltzes Chopin published himself—­“They must please; they are of another stamp than the usual waltzes, and in the style in which they can only be conceived by Chopin when he looks in a grandly-artistic way into the dancing crowd, which he elevates by his playing, thinking of other things than of what is being danced.”  In the A flat major waltz which bears the opus number 42, the duple rhythm of the melody along with the triple one of the accompaniment seems to me indicative of the loving nestling and tender embracing of the dancing couples.  Then, after the smooth gyrations of the first period, come those sweeping motions, free and graceful like those of birds, that intervene again and again between the different portions of the waltz.  The D flat major part bubbles over with joyousness.  In the sostenuto, on the other hand, the composer becomes sentimental, protests, and heaves sighs.  But at the very height of his rising ardour he suddenly plunges back into that wild, self-surrendering, heaven and earth-forgetting joyousness—­a stroke of genius as delightful as it is clever.  If we do not understand by the name of scherzo a fixed form, but rather a state of mind, we may say that Chopin’s waltzes are his scherzos and not the pieces to which he has given that name.  None of Chopin’s waltzes is more popular than the first of Op. 64 (in D flat major).  And no wonder!  The life, flow, and oneness are unique; the charm of the multiform motions is indescribable.  That it has been and why it has been called valse au petit chien need here only be recalled to the reader’s recollection (see Chapter XXVI., p. 142).  No. 2 (in C sharp minor); different as it is, is in its own way nearly as perfect as No. 1.  Tender, love-sick longing cannot be depicted more truthfully, sweetly, and entrancingly.  The excellent No. 3 (in A flat major), with the exquisite serpentining melodic lines, which play so important a part in Chopin’s waltzes, and other beautiful details, is in a somewhat trying position beside the other two waltzes.  The non-publication by the composer of the waltzes which have got into