Phthora nenano (Medieval Greek: φθορὰ νενανῶ, also νενανὼ) is the name of one of the two "extra" modes in the Byzantine Octoechos—an eight-mode system, which was proclaimed by a synod of 792 (1233 years ago) (792). The phthorai nenano and nana were favoured by composers at the Monastery Agios Sabas, near Jerusalem, while hymnographers at the Stoudiou-Monastery obviously preferred the diatonic mele.

Today the system of eight diatonic modes and two phthorai ("destroyers") is regarded as the modal system of Byzantine chant, and during the eighth century it became also model for the Latin tonaries—introductions into a proper diatonic eight mode system and its psalmody, created by Frankish cantores during the Carolinigian reform. While φθορά νενανῶ was often called "chromatic", the second phthora was named "nana" (gr. φθορά νανὰ) and called "enharmonic", the names were simply taken from the syllables used for the intonation (enechema). The two phthorai were regarded as two proper modes, but also used as transposition or alteration signs. Within the diatonic modes of the octoechos they cause a change into another (chromatic or enharmonic) genus (metavoli kata genos).

The earliest description of phthora nenano and of the eight mode system (octoechos) can be found in the Hagiopolites treatise which is known in a complete form through a fourteenth-century manuscript. The treatise itself can be dated back to the ninth century, when it introduced the book of tropologion, a collection of troparic and heirmologic hymns which was ordered according to the eight-week cycle of the octoechos. The first paragraph of the treatise maintains, that it was written by John of Damascus. The hymns of the tropologion provided the melodic models of one mode called echos (gr. ἦχος), and models for the phthora nenano appeared in some mele of certain echoi like protos and plagios devteros.

—Hagiopolites (§2)

The author of the treatise wrote obviously during or after the time of Joseph and his brother Theodore the Studite, when the use the mesos forms, phthorai nenano and nana were no longer popular. The word "mousike" (μουσική) referred an autochthonous theory during the 8th century used by the generation of John of Damascus and Cosmas of Maiuma at Mar Saba, because it was independent from ancient Greek music. But it seems that it was regarded as inappropriate to use these phthorai for the hymn melodies composed by Joseph and other hymns composed since the ninth century, since they must have preferred the diatonic octoechos based on the kyrios and the plagios instead of the mesoi.

The concept of phthora in the Hagiopolites was less concerned that the Nenano and Nana were somehow bridges between the modes. As an introduction of the tropologion it had to integrate the mele composed in these phthorai within the octoechos order and its weekly cycles. Since they had their own mele and compositions like the other echoi, they were subordinated to the eight diatonic echoi according to the pitches or degrees of the mode (phthongoi) of their cadences.

{{Text and translationφθοραὶ δὲ ὠνομασθήσαν, ὅτι ἐκ τῶν ἰδίων ἤχων  πᾶρχονται, τελειοῦνται δὲ εἰς ἑτέρων ἤχων φθογγὰς αἱ θέσεις αὐτῶν καὶ τὰ  ποτελέσματα. |They were called Phthorai (i.e. destroyers), because they begin from their own Echoi, but the thesis of their cadences and formulas are on notes (phthongoi) from other Echoi. |Hagiopolites (§34)}}

They had to be classified according to a certain echos of the eight-week cycle by adding the intonation "nenano" to the intonation of the main diatonic echos (usually abbreviated by a modal signature). For example, the intonation formula of echos plagios devteros (E) could be followed by the intonation of nenano which leads to the echos protos (a), as a kind of "mesos devteros", which lies in between the finalis of the kyrios (b natural) and the one of its plagios (E). Usually the diatonic kyrios protos (a) could end on its plagios (D) in the diatonic genus, but the chromatic phthora nenano makes it end in the plagios devteros (E).