Connection between みっか/むいか and よっか/ようか


The pronunciation of [三日]{みっか} and [六日]{むいか}, the 3rd and 6th days of the
month, are very similar, as are [四日]{よっか} and [八日]{ようか}, the 4th and 8th days
of the month. Is there any inherent significance to that? That is, was there
historically any etymological process like infixing a glottal stop (or the
historical predecessor of っ) or ablaut to derive the name of the 2n-th day of
the month from the n-th day? I'm thinking about something like the etymology
of 'eleven' and 'twelve' in English, which came from longer words that were
approximately 'one left' and 'two left'. I haven't run across any productive
process for doubling numbers in other languages, though (especially small
ones); is this just a coincidence or convergent evolution?




Here is how people counted numbers up to ten in archaic Japanese:

[code]

    number    n-th day         (modern Japanese)
    --------  ---------------  -----------------
    ひとつ    ひとひ/ついたち  ついたち
    ふたつ    ふつか           ふつか
    みつ      みか             みっか
    よつ      よか/ようか      よっか
    いつつ    いつか           いつか
    むつ      むゆか           むいか
    ななつ    なぬか           なのか
    やつ      やうか           ようか
    ここのつ  ここぬか         ここのか
    とを      とをか           とおか
    
[/code]

So these day names except for 1日 were directly derived from `number + か`,
although they underwent some sound changes. Notably, many vowels before か were
turned to "u" (eg, fut **a** tsu → fut **u** ka, nan **a** tsu → nan **u** ka,
kokon **o** tsu → kokon **u** ka). In addition, many やう sounds were later
changed to よう (eg きゃう(京) → きょう, やうやう(漸う) → ようよう), and that's probably why the
sound of 8日 became even closer to that of 4日.

Ultimately, your question is about simple numbers. Are there any relationships
between みつ (3) vs むつ (6), and よつ (4) vs やつ (8)? Actually, some people suspect
that they are etymologically related, because むつ can be considered as "double
みつ", and やつ as "double よつ". According to [『和力:
日本を象る』](https://books.google.co.jp/books?id=1Kalz7-zvTAC&lpg=PT278&ots=4TufSrExGa&dq=%E3%81%84%E3%81%A4%E3%81%A4%E3%80%80%E3%82%80%E3%81%A3%E3%81%A4%20%E8%AA%9E%E6%BA%90%20%E5%80%8D&hl=ja&pg=PT278#v=onepage&q=%E3%81%84%E3%81%A4%E3%81%A4%E3%80%80%E3%82%80%E3%81%A3%E3%81%A4%20%E8%AA%9E%E6%BA%90%20%E5%80%8D&f=false):

>
> 「みっつ」と「むっつ」は語幹が「ｍ」、「よっつ」と「やっつ」は「ｙ」（略）とすると、語幹が同じ子音同士の意味する数値が、倍の関係になっている、という指摘である。つまり、「ｍ」が三と六、「ｙ」が四と八、「ｔ」が五と十となり、それぞれが一：二の関係になっている

This seems to be only a hypothesis. These numbers have been used since long
before Japanese people learned how to write characters. It must be very
difficult to make a definitive conclusion.

Finally, please note that よっか and ようか sound very different to the ears of
native Japanese speaker today. Speech recognition software like _Siri_ is
often bad at distinguishing these, but the chance of misunderstanding in
human-to-human conversations is reasonably low.




Here is how people counted numbers up to ten in archaic Japanese:

[code]

    number    n-th day         (modern Japanese)
    --------  ---------------  -----------------
    ひとつ    ひとひ/ついたち  ついたち
    ふたつ    ふつか           ふつか
    みつ      みか             みっか
    よつ      よか/ようか      よっか
    いつつ    いつか           いつか
    むつ      むゆか           むいか
    ななつ    なぬか           なのか
    やつ      やうか           ようか
    ここのつ  ここぬか         ここのか
    とを      とをか           とおか
    
[/code]

So these day names except for 1日 were directly derived from `number + か`,
although they underwent some sound changes. Notably, many vowels before か were
turned to "u" (eg, fut **a** tsu → fut **u** ka, nan **a** tsu → nan **u** ka,
kokon **o** tsu → kokon **u** ka). In addition, many やう sounds were later
changed to よう (eg きゃう(京) → きょう, やうやう(漸う) → ようよう), and that's probably why the
sound of 8日 became even closer to that of 4日.

Ultimately, your question is about simple numbers. Are there any relationships
between みつ (3) vs むつ (6), and よつ (4) vs やつ (8)? Actually, some people suspect
that they are etymologically related, because むつ can be considered as "double
みつ", and やつ as "double よつ". According to [『和力:
日本を象る』](https://books.google.co.jp/books?id=1Kalz7-zvTAC&lpg=PT278&ots=4TufSrExGa&dq=%E3%81%84%E3%81%A4%E3%81%A4%E3%80%80%E3%82%80%E3%81%A3%E3%81%A4%20%E8%AA%9E%E6%BA%90%20%E5%80%8D&hl=ja&pg=PT278#v=onepage&q=%E3%81%84%E3%81%A4%E3%81%A4%E3%80%80%E3%82%80%E3%81%A3%E3%81%A4%20%E8%AA%9E%E6%BA%90%20%E5%80%8D&f=false):

>
> 「みっつ」と「むっつ」は語幹が「ｍ」、「よっつ」と「やっつ」は「ｙ」（略）とすると、語幹が同じ子音同士の意味する数値が、倍の関係になっている、という指摘である。つまり、「ｍ」が三と六、「ｙ」が四と八、「ｔ」が五と十となり、それぞれが一：二の関係になっている

This seems to be only a hypothesis. These numbers have been used since long
before Japanese people learned how to write characters. It must be very
difficult to make a definitive conclusion.

Finally, please note that よっか and ようか sound very different to the ears of
native Japanese speaker today. Speech recognition software like _Siri_ is
often bad at distinguishing these, but the chance of misunderstanding in
human-to-human conversations is reasonably low.

