[25.11 ...] He men oun [12] barytate chromatike lichanos tes [13] enarmoniou barytates hektoi merei to-[14]nou oxytera estin. [25.11 ...]Thus the [12] lowest chromatic lichanos from [13] the lowest enharmonic a sixth part of a tone [14] is higher.
epeideper he chro-[15]matike diesis tes enarmoniou dieseos [16] dodekatemorioi tonou meizon esti. since the chromatic [15] diesis from the enharmonic diesis [16] by a twelfth part of a tone is greater.
Dei [17] gar to tou autou tritemorion tou tetartou [18] merous dodekatemorioi hyperechein. A [17] third part of anything from a quarter of the [18] same thing a twelfth-part must exceed.
[19] hai de duo chromatikai ton duo [20] enarmonion delon hos toi diplasioi. [19] and the two chromatics from the two [20] enharmonics evidently must double that.
[21] touto de estin hektemorion elatton dia-[22]stema tou elachistou ton meloidoume-[23]non. [21] This is a sixth part, an interval smaller [22] than the least of the melodic [23] ones.
Ta de toiauta ameloideta [24] estin. ameloideton gar legomen, ho me [25] tattetai kath' heauto en systemati. Such intervals are unmelodic, [24] since we call 'unmelodic' any [25] that is not placed in a systema.
He de [26] barytate diatonos tes barytates [27] chromatikos hemitonioi kai dodekate-[28]morioi tonou oxytera estin. The [26] lowest diatonic (lichanos) from the lowest [27] chromatic a semitone and a twelfth [28] part of a tone is higher.
epi men gar [29] ten tou hemioliou chromatos lichanon [30] hemitonion en ep' autes. We said that [29] from the hemiolic chromatic lichanos, [30] it is a semitone.
apo de tes hemio-[31]liou epi ten enarmonion, diesis. and from the hemiolic [31] to the enharmonic is a diesis.
apo [32] de tes enarmoniou epi ten baryta-[33]ten chromatiken, hektemorion. from [32] the enharmonic to the lowest [33] chromatic is a sixth part.
apo de [34] tes barytates chromatikes epi ten hemiolion, dodekatemorion tonou. from [34] the lowest chromatic to the hemiolic is a twelfth part of a tone.
to [26.1] de tetartemorion ek trion dodeka-[2]temorion synkeitai. Now [26.1] a quarter of three twelfth-[2]parts is composed.
host' einai phane-[3]ron, so that it is clear [3] that
hoti to eiremenon diastema estin [4] apo tes barytates diatonou, epi ten [5] barytaten chromatiken. it is the interval stated [4] from the lowest diatonic, to the [5] lowest chromatic.
he de syn-[6]tonotate diatonOS tes barytates [7] diatonou, diesei esti syntonotera. The tensest [6] diatonic (lichanos) from the lowest [7] diatonic is a diesis tenser.
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> Ek touton de phaneroi gignontai hoi topoi ton lichanon hekastes;
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The enharmonic genus --------------------
[1.24.15-21] > Touton houtos horismenon pros toi baryteroi ton > menonton phthongon eilephtho to elachiston pyknon; touto > d' estai to ek duo dieseon (enarmonion elachiston; epeita > deuteron pros toi autoi; touto de estai to ek duo dieseon) > chromatikon elachiston. esontai de (hai) duo li|chanoi > eilemmenai duo genon barytatai, he men harmonias he de chromatos. > >> let us take the smallest pyknon, placed next to the lower >> of the fixed notes. This will be the one composed of two >> enharmonic or two of the smallest chromatic diesis. The two >> lichanoi thus specified will be the lowest in each of the >> two genera, one in the enharmonic, the other in the chromatic:
Extracting what is relevant to this genus:
[1.24.15-21] >> let us take the ... _pyknon_ ... composed of two enharmonic >> ... dieses. The ... [_lichanos_] thus specified will be the >> lowest in ... the enharmonic [genus]. THIS ALREADY APPEARS ABOVE vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
[2.50.23-24] > Mia men oun ton diaipeseon estin enarmonios en he > to men pyknon hemitonion esti to | de loipon ditonon. > >> One of these divisions is enharmonic, in which the _pyknon_ >> is a semitone and the remainder a ditone.
> [2.50.22 ...] Mia men [23] oun ton diaipeseon estin enarmonios, > [24] en he to men pyknon, hemitonion esti; > to [25] de loipon, ditonon. > >> One of these divisions [of the tetrachord] is enharmonic, in >> which the pyknon is a semitone and the remainder a ditone. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Assuming the Pythagorean 'limma' 256/243 to be the 'semitone', and the 'enharmonic diesis' to be exactly half of this, we get:
