Bhashya
विष्णुं सर्वानुदात्तात्मिका गीतिः ।प्रथमस्य अन्त्यमिति, प्रथमपादोक्ताक्षरद्वयेऽपि अन्त्यम् अन्त्यस्वरयुक्तं जानीयादिति प्राक्तनमनुषज्यते ।मुखं सर्वानुदात्तात्मिका गीतिः द्वितीयस्य अन्त्यमिति, द्वितीयपादोक्ताक्षरद्वयेऽपि अन्त्यस्वरयुक्तं सामेति संबन्धः ।ननु सर्वोद्धारेषु प्रथमद्वितीयशब्दौ कस्मात्पादाभिप्रायेण व्याख्यायेते, न उक्ताक्षरसंख्यापेक्षया ? तथा हि, प्रथमान्त्यमिति उक्ताक्षरद्वयमध्ये प्रथमस्याक्षरस्य अन्त्यं स्वरं जानीयादिति ।तथा द्वितीयान्त्यमिति उक्ताक्षरद्वयमध्ये द्वितीयस्याक्षरस्य अन्त्यं स्वरं जानीयात् ।एवं प्रथमोद्धारेऽपि प्रथमस्याक्षरस्य द्वितीयस्याक्षरस्य आद्यस्वरं जानीयादिति कस्मान्न व्याख्यायते ? उच्यते ।सर्वत्र हि अक्षरद्वयमुक्त्वैव प्रथमद्वितीयतृतीयचतुर्थशब्दाः श्रूयन्ते ।न हि अक्षरद्वयोक्तौ तृतीयचतुर्थशब्दावुपपन्नौ, तृतीयचतुर्थयोरक्षरयोरभावात्, इति पादाभिप्रायेण व्याख्येयाविति निश्चिते, तत्साहचर्यात्प्रथमद्वितीयशब्दावक्षरद्वयोक्तावुपपन्नाविति न अक्षराभिप्रायेण व्याख्येयौ ; किं तु पादाभिप्रायेणैवेति स्थितम् ।भद्रम्, सर्वानुदात्तात्मिका गीतिः तृतीयस्य अन्त्यमित्युक्तार्थम् ।म्यहम्, सर्वानुदात्तात्मिका गीतिः चतुर्थस्य अन्त्यमित्युक्तार्थम् ।
In plain words
'Viṣṇu' is a note pitched entirely low. Its name: the last piece of the first line. Even here, within the pair of syllables the first line gives, it's the very last one — carrying the final pitch — that becomes the chant; the same rule already given simply carries forward. 'Mukham' is the same low-pitched note, and it's the last piece of the second line — again, the syllable carrying the final pitch of that pair, understood as the Sāman. Now, someone objects: why explain 'first' and 'second' by which line they come from, rather than by which syllable — first or second — in the pair itself? After all, 'the last of the first' could just as easily mean the last sound of the first syllable in the pair, and 'the last of the second' the last sound of the second syllable. And if that's how we read it here, why wasn't the earlier extraction read the same way — the first sound of the first syllable, the first sound of the second? Here's the answer: every single time, the pair of syllables is named first, and only then do the words 'first,' 'second,' 'third,' 'fourth' appear. But 'third' and 'fourth' cannot possibly refer to syllables within a pair — a pair has no third or fourth member. So 'third' and 'fourth' must mean the third and fourth lines. And once that's settled, 'first' and 'second' fall in line with them — even though, taken alone, they could have meant the first and second syllable of the pair, they don't; they mean the first and second lines too, exactly like their neighbors. 'Bhadram' is the same low note — the last piece of the third line, as already explained. And 'Myaham' is the same low note again — the last piece of the fourth line, as already explained.
Close to the Sanskrit
'Viṣṇum' is the melody entirely on the grave tone. '[It is] the last of the first' — that is its name; even within the pair of syllables stated in the first foot, it is the last syllable — endowed with the last tone — that one should know as the Sāman; this is carried over from what was said before. 'Mukham' is the melody entirely on the grave tone; '[it is] the last of the second' — even within the pair of syllables stated in the second foot, what is meant is the syllable endowed with the last tone; 'Sāman' — that is the understood connection. Objection: in all these extractions, why are the words 'first' and 'second' explained with reference to the foot, and not with reference to the numbered position among the stated syllables? That is: 'the last of the first' would then mean — among the stated pair of syllables — one should know the last tone of the first syllable. Likewise, 'the last of the second' would mean, among the stated pair, one should know the last tone of the second syllable. Then why, in the first extraction too, is it not likewise explained that one should know the first tone of the first syllable and of the second syllable respectively? It is answered: everywhere, only after stating a pair of syllables are the words 'first,' 'second,' 'third,' and 'fourth' heard. For, once only a pair of syllables has been stated, the words 'third' and 'fourth' would not fit, since there is no third or fourth syllable in a pair. This being settled — that they must be explained with reference to the foot — by association with that, the words 'first' and 'second,' even though they would fit a syllable-count reading too, are not to be explained with reference to the syllable; rather, it stands settled that they too are explained with reference to the foot alone. 'Bhadram' is the melody entirely on the grave tone; '[it is] the last of the third' — already explained. 'Myaham' is the melody entirely on the grave tone; '[it is] the last of the fourth' — already explained.