# Talk:♠/Slide whistles and harmony

## When be become a band...

I have a few ideas:

1. Soon we will start to play chords. Perhaps transposing from this
2. I once saw a colleague in a plasma lab open a bottle of chemically pure "ethanol" and discover that it actually contained benzene. Never trust a chemical that is pure enough for science to be safe enough to drink. I suggest we instead use this to clean the whistles.
3. We should do this with only fractions, and get them right:
```1-do         1
2-re-II      ??
3-mi-majIII  5/4 (the minIII is 6/5)
4-fa-IV      4/3
5-so-V       3/2
6-la-VI      5/3

```

What is the second?

• (4/3)×(5/6)= 10/9 -- Minor third from the fourth
• (3/2)× (3/4) = 9/8 -- Fourth from the fifth
• (5/3) × (2/3) = 10/9 -- Fifth from the sixth

Almost all music we listen to is based on the approximation that 10/9 ≈ 9/8, or cross-multiplying, that 81≈80.

--Guy vandegrift (discusscontribs) 14:17, 18 October 2017 (UTC)

## What are the most harmonious intervals in the first octave?

```{3/2, 4/3, 5/3, 5/4, 6/5, 7/4, 7/5, 7/6, 8/5, 8/7}
V    IV   VI  III  iii  *     ?    ?   vi    ?
```

Here I used capital romans for major and lower case for minor. The 7/5 is the devil's triad.

## Two images

I made these on Saturday.--Guy vandegrift (discusscontribs) 01:56, 22 October 2017 (UTC)

The major second can be constructed in one of two ways, once the the important natural consonant ratios are determined: One can either go up a perfect fifth and down a w:perfect fourth, or go up a major sixth and down a major third. The resulting fractions are slightly different.
A systematic ordering of rational fractions between 1 and 2 are shown. The boxed ratios correspond to the major third., perfect fourth, perfect fifth and major sixth of a major scale. The rounded boxes correspond to accidentals that are minor intervals from the tonic.
• The equal tempered and the 7:4 natural are both available on commons: