16:20:25/(225/224)：修订间差异

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创建页面，内容为“'''15间增三和弦'''是一个15间律下的本质调和和弦。在密集排列下，根音与中音，中音与冠音的距离均为大小约5/4的三度，根音与冠音的距离的距离约为14/9，因为这个和弦要求调和15间差。 在2.3.5.7/(81/80,225/224)下 In meantone this triad consists of two major thirds and a diminished fourth, the classic augmented triad of the meantone era. It can also be described as…”
 
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'''15间增三和弦'''是一个[[15间律]]下的本质调和和弦。在密集排列下，根音与中音，中音与冠音的距离均为大小约[[5/4]]的三度，根音与冠音的距离的距离约为[[14/9]]，因为这个和弦要求调和15间差。
'''15间增三和弦'''是一个[[15间律|2.3.5.7/(225/224)]]下的本质调和和弦。它的频率比为1/1-5/4-25/16.


在[[7限中全律|2.3.5.7/(81/80,225/224)]]下
在密集排列下，根音与中音，中音与冠音的距离均为大小约[[5/4]]的三度，根音与冠音的距离的距离约为[[14/9]]，因为这个和弦要求调和15间差。


在[[2.3.5.7/(81/80,225/224)|7限中全律]]下，这一和弦包含两个大三度和一个增五度——这也就是传统的增三和弦。


In meantone this triad consists of two major thirds and a diminished fourth, the classic augmented triad of the meantone era. It can also be described as a marvel-tempered version of a 1–5/4–14/9 chord.
为了使得7限效果更强，可以在根音下方加入一个频率为2/3的音，也就是2/3-1/1-5/4-25/16. 这样，最低音与最高音的频率比是[[7/3]]，这是比14/9更简单的音程。


The 9-odd-limit marvel chords are of pattern 1b, meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures. In this article, voicing with the perfect fifth is prioritized.
== 另见 ==


The three 9-odd-limit marvel triads are
[[16:20:25]] —— 标准增三和弦


The aforementioned marvel augmented triad;
[[16:20:25/(128/125)]] —— 3ed2的增三和弦
1–5/4–7/5 with steps 5/4, 9/8, 10/7, and its inverse
1–9/8–7/5 with steps 9/8, 5/4, 10/7.
marvel.jpg
Marvel triad
The six 9-odd-limit marvel tetrads are
 
1–5/4–7/5–7/4 with steps 5/4, 9/8, 5/4, 8/7;
1–9/8–5/4–7/5 with steps 9/8, 10/9, 9/8, 10/7;
1–5/4–7/5–14/9 with steps 5/4, 9/8, 10/9, 9/7, and its inverse
1–9/8–7/5–9/5 with steps 9/8, 5/4, 9/7, 10/9;
1–9/8–7/5–7/4 with steps 9/8, 5/4, 5/4, 8/7, and its inverse
1–5/4–7/5–8/5 with steps 5/4, 9/8, 8/7, 5/4.
The last four tetrads contain the marvel augmented triad.
 
The two 9-odd-limit marvel pentads are:
 
1–9/8–5/4–7/5–7/4 with steps 9/8, 10/9, 9/8, 5/4, 8/7, and its inverse
1–9/8–5/4–7/5–8/5 with steps 9/8, 10/9, 9/8, 8/7, 5/4.
If we allow the 15-odd-limit, there are many more possibilities. One notable 15-odd-limit tetrad is 1–4/3–3/2–15/8 which has as its homonym 1–9/8–7/5–3/2.
 
Equal temperaments with marvel chords include 19, 22, 31, 41, 43, 50, 53, 72, 84, 94, 103, 166 and 197.

2025年12月3日 (三) 15:34的版本

15间增三和弦是一个2.3.5.7/(225/224)下的本质调和和弦。它的频率比为1/1-5/4-25/16.

在密集排列下，根音与中音，中音与冠音的距离均为大小约5/4的三度，根音与冠音的距离的距离约为14/9，因为这个和弦要求调和15间差。

在7限中全律下，这一和弦包含两个大三度和一个增五度——这也就是传统的增三和弦。

为了使得7限效果更强，可以在根音下方加入一个频率为2/3的音，也就是2/3-1/1-5/4-25/16. 这样，最低音与最高音的频率比是7/3，这是比14/9更简单的音程。

另见

16:20:25 —— 标准增三和弦

16:20:25/(128/125) —— 3ed2的增三和弦

检索自“https://tun.wiki/index.php?title=16:20:25/(225/224)&oldid=61”