{ "cells": [ { "attachments": {}, "cell_type": "markdown", "id": "ee1b27f0-32a1-42b0-be45-bfd6af50d259", "metadata": {}, "source": [ "# 課題\n", "\n", "## ピタゴラス音律がルネッサンス以降に平均律に取って代わられた理由を考える" ] }, { "attachments": {}, "cell_type": "markdown", "id": "df9a8dfc-ed1d-4b6b-aae7-f8bb54ce1fba", "metadata": {}, "source": [ "* [Pythagorean tuning - Wikipedia](https://en.wikipedia.org/wiki/Pythagorean_tuning)\n", " * [How Pythagoras Broke Music (and how we kind of fixed it) [see comments for corrections] - YouTube](https://www.youtube.com/watch?v=EdYzqLgMmgk)\n", " - [Pythagorean comma - Wikipedia](https://en.wikipedia.org/wiki/Pythagorean_comma)\n", " - [Wolf interval - Wikipedia](https://en.wikipedia.org/wiki/Wolf_interval)\n", "* [Equal temperament - Wikipedia](https://en.wikipedia.org/wiki/Equal_temperament)" ] }, { "attachments": {}, "cell_type": "markdown", "id": "7b9e54ba-ee47-4438-80e9-30e7395e181b", "metadata": {}, "source": [ "## FMPの \"Pythagorean Tuning\" を参照する\n", "\n", "* [C1E10: Pythagorean Tuning](https://www.audiolabs-erlangen.de/resources/MIR/FMP/C1/C1E10_PythagoreanTuning.html)" ] }, { "cell_type": "code", "execution_count": 1, "id": "b95c5091-8950-4b66-932f-65d089e2241a", "metadata": { "tags": [] }, "outputs": [], "source": [ "import numpy as np\n", "import IPython.display as ipd\n", "import matplotlib.pyplot as plt\n", "import libfmp.c1\n", "import librosa" ] }, { "cell_type": "code", "execution_count": 2, "id": "6b8a9709-fb3b-4e8d-b0f8-2b2278918b2f", "metadata": { "tags": [] }, "outputs": [], "source": [ "import pandas as pd\n", "from collections import OrderedDict\n", "\n", "# Computation of frequencies and differences\n", "pyt_frac = ['1:1', '$2^8:3^5$', '$3^2:2^3$', '$2^5:3^3$', '$3^4:2^6$', '$2^2:3$', '$3^6:2^9$', \n", " '$3:2$', '$2^7:3^4$', '$3^3:2^4$', '$2^4:3^2$', '$3^5:2^7$', '$2:1$']\n", "pyt_ratio = np.asarray([1, 256/243, 9/8, 32/27, 81/64, 4/3, 729/512, 3/2, 128/81, 27/16, 16/9, 243/128, 2])\n", "p = 60\n", "freq = libfmp.c1.f_pitch(p)\n", "freq_pyt = pyt_ratio * freq\n", "notes = np.asarray(range(p, p + 13))\n", "freq_center = libfmp.c1.f_pitch(notes)\n", "freq_deviation_cents = libfmp.c1.difference_cents(freq_pyt, freq_center)\n", "\n", "# Generation of sinusoids\n", "dur = 4 # seconds\n", "Fs = 4000 # sampling rate\n", "\n", "sinusoid_freq_center = []\n", "for freq in freq_center:\n", " x, t = libfmp.c1.generate_sinusoid(dur=dur, Fs=Fs, freq=freq)\n", " sinusoid_freq_center.append(x)\n", "\n", "sinusoid_freq_pyt = []\n", "for freq in freq_pyt:\n", " x, t = libfmp.c1.generate_sinusoid(dur=dur, Fs=Fs, freq=freq)\n", " sinusoid_freq_pyt.append(x)" ] }, { "cell_type": "code", "execution_count": 3, "id": "b7bba224-aac3-4561-a770-2210933e5ad9", "metadata": { "tags": [] }, "outputs": [], "source": [ "# Generation of sinusoids\n", "dur = 4 #seconds\n", "Fs = 4000 #sampling rate" ] }, { "cell_type": "code", "execution_count": 4, "id": "13b63b93-450b-4fbc-8bf1-87081482c8db", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/html": [ "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
NoteET Freq. (Hz)ET SinusoidPyt. RatioPyt. Freq. (Hz)Pyt. SinusoidDifference (Cents)
1C4261.631:1261.630.00
2C$^\\sharp$4277.18$2^8:3^5$275.62-9.78
3D4293.66$3^2:2^3$294.333.91
4D$^\\sharp$4311.13$2^5:3^3$310.07-5.87
5E4329.63$3^4:2^6$331.127.82
6F4349.23$2^2:3$348.83-1.96
7F$^\\sharp$4369.99$3^6:2^9$372.5111.73
8G4392.00$3:2$392.441.96
9G$^\\sharp$4415.30$2^7:3^4$413.43-7.82
10A4440.00$3^3:2^4$441.495.87
11A$^\\sharp$4466.16$2^4:3^2$465.11-3.91
12B4493.88$3^5:2^7$496.689.78
13C4523.25$2:1$523.250.00
" ], "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sinusoid_freq_center = []\n", "for freq in freq_center:\n", " x, t = libfmp.c1.generate_sinusoid(dur=dur, Fs=Fs, freq=freq)\n", " sinusoid_freq_center.append(x)\n", "\n", "sinusoid_freq_pyt = []\n", "for freq in freq_pyt:\n", " x, t = libfmp.c1.generate_sinusoid(dur=dur, Fs=Fs, freq=freq)\n", " sinusoid_freq_pyt.append(x)\n", "\n", "# Generation of html table\n", "audio_tag_html_center = []\n", "for i in range(len(freq_center)):\n", " audio_tag = ipd.Audio(sinusoid_freq_center[i], rate=Fs)\n", " audio_tag_html = audio_tag._repr_html_().replace('\\n', '').strip()\n", " audio_tag_html = audio_tag_html.replace('\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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" ] }, "metadata": { "image/png": { "height": 190, "width": 789 } }, "output_type": "display_data" } ], "source": [ "# 平均律 (C4+G4)\n", "x1 = sinusoid_freq_center[0]+sinusoid_freq_center[7]\n", "# x1 += sinusoid_freq_center[4]\n", "ipd.display(ipd.Audio(x1, rate=Fs))\n", "libfmp.b.plot_signal(x1, Fs=Fs, figsize=(8, 2))\n", "plt.show()\n", "plot_spectrogram(x1, Fs=Fs, N=4096, H=1024, figsize=(8, 2))" ] }, { "attachments": {}, "cell_type": "markdown", "id": "a125fec7-40a9-47f9-971d-b08c7d0ed699", "metadata": {}, "source": [ "### 完全五度の根音を設定可能にした" ] }, { "cell_type": "code", "execution_count": 16, "id": "c1274cb1-3cb7-43e3-acbd-fea1b71f141a", "metadata": { "tags": [] }, "outputs": [], "source": [ "# 0 から 5 まで\n", "root = 4" ] }, { "cell_type": "code", "execution_count": 17, "id": "9ce63062-d7e5-4e4b-9884-b75c8d4daff3", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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" ] }, "metadata": { "image/png": { "height": 190, "width": 789 } }, "output_type": "display_data" } ], "source": [ "# ピタゴラス音律\n", "x2 = sinusoid_freq_pyt[root]+sinusoid_freq_pyt[(root+7) % 12]*((root+4)//12+1)\n", "# x2 += +sinusoid_freq_pyt[(root+4) % 12]*((root+4)//12+1)\n", "ipd.display(ipd.Audio(x2, rate=Fs))\n", "libfmp.b.plot_signal(x2, Fs=Fs, figsize=(8, 2))\n", "plt.show()\n", "plot_spectrogram(x2, Fs=Fs, N=4096, H=1024, figsize=(8, 2))" ] }, { "cell_type": "code", "execution_count": 18, "id": "d5309093-79f8-44fb-8fd9-f19efbb5d043", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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" ] }, "metadata": { "image/png": { "height": 190, "width": 789 } }, "output_type": "display_data" } ], "source": [ "# 平均律\n", "x3 = sinusoid_freq_center[root]+sinusoid_freq_center[(root+7) % 12]*((root+4)//12+1)\n", "# x3 += +sinusoid_freq_center[(root+4) % 12]*((root+4)//12+1)\n", "ipd.display(ipd.Audio(x3, rate=Fs))\n", "libfmp.b.plot_signal(x3, Fs=Fs, figsize=(8, 2))\n", "plt.show()\n", "plot_spectrogram(x3, Fs=Fs, N=4096, H=1024, figsize=(8, 2))" ] }, { "attachments": {}, "cell_type": "markdown", "id": "b8e59f5c-359a-4d56-b771-508599b2e185", "metadata": {}, "source": [ "## 三和音\n", "\n", "* [Triad (music) - Wikipedia](https://en.wikipedia.org/wiki/Triad_(music))\n", " - major triads (0–4–7)" ] }, { "cell_type": "code", "execution_count": 19, "id": "f4aa76c3-da0e-407d-a2b9-5398e76084ae", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "image/png": { "height": 190, "width": 789 } }, "output_type": "display_data" } ], "source": [ "# 平均律 (C4+E4+G4)\n", "x1 = sinusoid_freq_center[0]+sinusoid_freq_center[7]\n", "x1 += sinusoid_freq_center[4]\n", "ipd.display(ipd.Audio(x1, rate=Fs))\n", "libfmp.b.plot_signal(x1, Fs=Fs, figsize=(8, 2))\n", "plt.show()\n", "plot_spectrogram(x1, Fs=Fs, N=4096, H=1024, figsize=(8, 2))" ] }, { "attachments": {}, "cell_type": "markdown", "id": "40158654-374f-45df-bbdb-28e883da5f49", "metadata": {}, "source": [ "### 根音を選択可能にした" ] }, { "cell_type": "code", "execution_count": 21, "id": "66afc680-1311-4dfd-b7c3-d0653717c4da", "metadata": { "tags": [] }, "outputs": [], "source": [ "# 0 から 5まで\n", "root = 4" ] }, { "cell_type": "code", "execution_count": 22, "id": "a727cae8-1726-4d09-bc90-5a05a69737e7", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "image/png": { "height": 190, "width": 789 } }, "output_type": "display_data" } ], "source": [ "# ピタゴラス音律\n", "x2 = sinusoid_freq_pyt[root]+sinusoid_freq_pyt[(root+7) % 12]*((root+4)//12+1)\n", "x2 += +sinusoid_freq_pyt[(root+4) % 12]*((root+4)//12+1)\n", "ipd.display(ipd.Audio(x2, rate=Fs))\n", "libfmp.b.plot_signal(x2, Fs=Fs, figsize=(8, 2))\n", "plt.show()\n", "plot_spectrogram(x2, Fs=Fs, N=4096, H=1024, figsize=(8, 2))" ] }, { "cell_type": "code", "execution_count": 23, "id": "34b64f27-ca0d-4183-b4ee-f111d5fd0c4b", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "image/png": { "height": 190, "width": 789 } }, "output_type": "display_data" } ], "source": [ "# 平均律\n", "x3 = sinusoid_freq_center[root]+sinusoid_freq_center[(root+7) % 12]*((root+4)//12+1)\n", "x3 += +sinusoid_freq_center[(root+4) % 12]*((root+4)//12+1)\n", "ipd.display(ipd.Audio(x3, rate=Fs))\n", "libfmp.b.plot_signal(x3, Fs=Fs, figsize=(8, 2))\n", "plt.show()\n", "plot_spectrogram(x3, Fs=Fs, N=4096, H=1024, figsize=(8, 2))" ] }, { "attachments": {}, "cell_type": "markdown", "id": "a727bd96-301e-48c5-a8ea-d877042be72d", "metadata": {}, "source": [ "## 改めて課題\n", "\n", "完全五度と長三和音で根音の設定を変えてピタゴラス音律と平均律の波形を比較し、ルネッサンス以降に平均律と三和音が使われるようになった理由を考えてみる" ] }, { "cell_type": "code", "execution_count": 1, "id": "379e729f-7b49-4202-bc6c-eb6edd90c836", "metadata": {}, "outputs": [ { "data": { "text/markdown": [ "**ピタゴラス音律**とは、純粋な五度音程を基に作られた音律で、美しい倍音関係による和音を生み出します。しかし、その一方で、全てのキーで均等に美しい和音を得ることが難しいという欠点がありました。これは特に転調が多用されるようになった音楽にとって大きな問題でした。\n", "\n", "それに対して、**平均律**は全ての半音が均等な比率を持つように調律された音律です。このため、どのキーでも均等に美しい和音を得ることが可能となり、複雑な転調が可能になりました。\n", "\n", "ルネッサンス期以降の音楽は、複雑な転調や和声法が発展するにつれて、ピタゴラス音律の制約が問題となりました。このため、平均律が導入され、全てのキーで均一な和音関係を得ることが可能となりました。これにより、より複雑な音楽表現が可能となり、バロック音楽や古典派音楽などの発展を支えました。\n", "\n", "ただし、平均律は全ての音程を完全に均等にするため、一部の和音（特に三和音）は純粋な倍音関係からわずかにずれます。したがって、ピタゴラス音律に比べて和音の響きは少し劣るとも言えます。しかし、その差は微小であり、より複雑な音楽表現が可能となる利点がそれを上回ると考えられています。" ], "text/plain": [ "" ] }, "execution_count": 1, "metadata": { "text/markdown": { "jupyter_ai": { "custom_chain_id": "vioras" } } }, "output_type": "execute_result" } ], "source": [ "%%ai vioras\n", "ルネッサンス前後に、ピタゴラス音律から平均律に移行した理由を教えてください" ] }, { "cell_type": "code", "execution_count": 2, "id": "0d23d928-81c2-4f8d-8677-29c55bf71a0a", "metadata": {}, "outputs": [ { "data": { "text/markdown": [ "はい、あなたのおっしゃる通りです。ピタゴラス音律では、三和音（特に長三和音や短三和音）が\"唸り\"を生じることがあります。これは「コンマ」と呼ばれる微細な音程のずれによるものです。\n", "\n", "具体的には、ピタゴラス音律では完全五度を12回重ねて12音全てを生成しますが、その結果として得られる最後の音（すなわち、最初の音の倍音）と実際の2倍の音の間に微妙な音程のずれが生じます。このずれが「ピタゴラスのコンマ」と呼ばれています。\n", "\n", "このコンマにより、特に三和音を形成するときに、理論的には純粋な倍音関係にあるはずの音が微妙にずれ、結果として理想的な和音から唸り音が生じます。\n", "\n", "これに対して、平均律はこのコンマを各半音に分散させることで、どのキーでも同じ和音関係を維持します。これにより、どのキーでも同じように和音が鳴り、唸りを生じることなく転調が可能になります。\n", "\n", "したがって、ピタゴラス音律から平均律への移行は、音楽表現の幅を広げるための重要なステップでした。" ], "text/plain": [ "" ] }, "execution_count": 2, "metadata": { "text/markdown": { "jupyter_ai": { "custom_chain_id": "vioras" } } }, "output_type": "execute_result" } ], "source": [ "%%ai vioras\n", "ピタゴラス音律での三和音は、唸りを生じる場合があります" ] }, { "cell_type": "code", "execution_count": 3, "id": "0a0e832b-46f1-434c-9095-29412b85e177", "metadata": {}, "outputs": [ { "data": { "text/markdown": [ "あなたがおっしゃっている通り、ピタゴラス音律と平均律における三和音の違いは微細で、平均的な聴覚ではほとんど区別できません。実際、純粋な三和音（つまり、その音程が完全な整数比であるもの）を生み出す能力において、ピタゴラス音律は平均律よりも優れています。 \n", "\n", "しかし、問題となるのは転調やコード進行です。ピタゴラス音律は特定のキーに特化していますので、転調すると音程のバランスが崩れてしまいます。これに対して、平均律は全ての半音が同じ間隔で配置されているため、どのキーでも同じ和音と音程関係を維持することができます。これにより、音楽家は自由な転調やコード進行を行うことができ、音楽表現の幅が大いに広がりました。\n", "\n", "したがって、ピタゴラス音律から平均律への移行は、単に和音の美しさだけでなく、音楽表現全体の自由度を高めるための重要なステップだったと言えるでしょう。" ], "text/plain": [ "" ] }, "execution_count": 3, "metadata": { "text/markdown": { "jupyter_ai": { "custom_chain_id": "vioras" } } }, "output_type": "execute_result" } ], "source": [ "%%ai vioras\n", "三和音において、コンマのズレのないピタゴラス音律と平均律に大きな差はありません" ] }, { "cell_type": "code", "execution_count": null, "id": "e0d493be-4341-465d-924d-c1868cb69a47", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.8" } }, "nbformat": 4, "nbformat_minor": 5 }